##### Abstract

Combinatorial algebraic geometry comprises the parts of algebraic geometry where basic geometric phenomena can be described with combinatorial data, and where combinatorial methods are essential for further progress.

Research in combinatorial algebraic geometry utilizes combinatorial techniques to answer questions about geometry. Typical examples include predictions about singularities, construction of degenerations, and computation of geometric invariants such as Gromov-Witten invariants, Euler characteristics, the number of points in intersections, multiplicities, genera, and many more. The study of positivity properties of geometric invariants is one of the driving forces behind the interplay between geometry and combinatorics. Flag manifolds and Schubert calculus are particularly rich sources of invariants with positivity properties.

In the opposite direction, geometric methods provide powerful tools for studying combinatorial objects. For example, many deep properties of polytopes are consequences of geometric theorems applied to associated toric varieties. In other cases geometry is a source of inspiration. For instance, long-standing conjectures about matroids have recently been resolved by proving that associated algebraic structures behave as if they are cohomology rings of smooth algebraic varieties.

Much research in combinatorial algebraic geometry relies on mathematical software to explore and enumerate combinatorial structures and compute geometric invariants. Writing the required programs is a considerable part of many research projects. The development of new mathematics software is therefore prioritized in the program.

The program will bring together experts in both pure and applied parts of mathematics as well mathematical programmers, all working at the confluence of discrete mathematics and algebraic geometry, with the aim of creating an environment conducive to interdisciplinary collaboration. The semester will include four week-long workshops, briefly described as follows.

• A 'boot-camp' aimed at introducing graduate students and early-career researchers to the main directions of research in the program.
• A research workshop dedicated to geometry arising from flag manifolds, classical and quantum Schubert calculus, combinatorial Hodge theory, and geometric representation theory.
• A research workshop dedicated to polyhedral spaces and tropical geometry, toric varieties, Newton-Okounkov bodies, cluster algebras and varieties, and moduli spaces and their tropicalizations.
• A Sage/Oscar Days workshop dedicated to development of programs and software libraries useful for research in combinatorial algebraic geometry. This workshop will also feature a series of lectures by experts in polynomial computations.

#### Confirmed Speakers & Participants

• Speaker
• Poster Presenter
• Attendee
• Virtual Attendee
• Abdulafeez Abdulkareem
University of Africa Toru Orua
Feb 1-5, 2021
University of Iowa
Mar 22-26, 2021
• Simonetta Abenda
Università di Bologna
Feb 1-5, 2021; Feb 15-19, 2021
Stanford University
Feb 15-19, 2021
• Dan Abramovich
Brown University
Feb 1-May 7, 2021
UC Davis
Feb 1-May 7, 2021
Feb 1-May 7, 2021
• Rizal Afgani
Institut Teknologi Bandung
Apr 12-16, 2021
• Daniele Agostini
Max Planck Institute for Mathematics in the Sciences
Feb 1-5, 2021
• Daniele Agostini
Max Planck Institute for Mathematics in the Sciences
Feb 1-5, 2021
• Huda Ahmed
New York University
Feb 1-5, 2021
• Florian Aigner
Université du Québec à Montréal
Feb 1-5, 2021
• Tair Akhmejanov
University of California-Davis
Feb 1-May 7, 2021
• Edvard Aksnes
University of Oslo
Apr 12-16, 2021
• Doriann Albertin
Université Gustave Eiffel
Feb 1-5, 2021; Apr 12-16, 2021
• Elie Alhajjar
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Ayah Almousa
Cornell University
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Kamyar Amini
Sharif University of Technology
Feb 24-May 7, 2021
• David Anderson
Ohio State University
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Mar 31-May 5, 2021; Apr 12-16, 2021
• Nicholas Anderson
Queen Mary University of London
Apr 12-16, 2021
• Federico Ardila
San Francisco State University
Feb 1-May 31, 2021
Aalto University
Apr 12-16, 2021
• Veronica Arena
Brown University
Feb 1-5, 2021
• Xerxes Arsiwalla
Pompeu Fabra University & Wolfram Research
Feb 1-5, 2021; Apr 12-16, 2021
• Ahmed Umer Ashraf
University of Western Ontario
Feb 1-May 7, 2021
• Faqruddin Azam
Oklahoma State University
Feb 1-5, 2021
• Olga Azenhas
University of Coimbra
Mar 10-May 5, 2021; Mar 22-26, 2021
• Christoph Baerligea
Beijing International Center for Mathematical Research
Feb 1-5, 2021
• Matthew Baker
Georgia Institute of Technology
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Esther Banaian
University of Minnesota
Feb 1-5, 2021
• Grant Barkley
Harvard University
Feb 3-5, 2021
• Gonzalo Barranco Mendoza
Apr 12-16, 2021
• Victor Batyrev
Universität Tübingnen
Apr 12-16, 2021
• Alexander Bauman
Brown University
Feb 1-5, 2021
• Dori Bejleri
Harvard University
Feb 1-5, 2021
• Prakash Belkale
University of North Carolina at Chapel Hill
Mar 22-26, 2021
• Mara Belotti
Technische Universität
Feb 1-5, 2021; Feb 15-19, 2021
• Carolina Benedetti V.
Feb 3-5, 2021
• Marko Berghoff
University of Oxford
Apr 12-16, 2021
• Joe Bernstein
North Dakota State University
Feb 1-5, 2021
• Marc Besson
University of North Carolina at Chapel Hill
Feb 1-5, 2021; Mar 22-26, 2021
University of Southern California
Feb 3-5, 2021
• Dhruv Bhatia
Brown University
Feb 1-5, 2021
• Shivam Bhatt
University of Toronto
Apr 12-16, 2021
• Christin Bibby
Louisiana State University
Feb 1-May 7, 2021
• Sara Billey
University of Washington
Feb 1-May 7, 2021
• Simone Billi
University of Bologna
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Aram Bingham
Tulane University
Feb 1-5, 2021; Feb 15-19, 2021; Mar 17-May 5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Rekha Biswal
Universite Laval
Mar 22-26, 2021
• Alex Black
UC Davis
Feb 1-5, 2021; Apr 12-16, 2021
• Kenneth Blakey
Brown University
Feb 1-5, 2021
• Andreas Blatter
University of Bern
Feb 1-5, 2021
• Lev Blechman
Tel Aviv university
Feb 1-5, 2021
• Thomas Blomme
Université de Neuchâtel
Feb 1-5, 2021
• Janko Boehm
TU Kaiserslautern
Feb 15-19, 2021
• Narasimha Chary Bonala
Ruhr University of Bochum
Apr 12-16, 2021
• Jonathan Boretsky
Harvard University
Feb 1-5, 2021
• Alessio Borzì
University of Warwick
Feb 1-5, 2021
• Lara Bossinger
Mathematics Institute UNAM, Oaxaca
Feb 1-5, 2021; Apr 12-16, 2021
• Alin Bostan
INRIA
Feb 15-19, 2021
University of Massachusetts Amherst
Mar 22-26, 2021; Apr 12-16, 2021
Brown University
Feb 1-May 7, 2021; Apr 11-17, 2021
• Sarah Brauner
University of Minnesota
Feb 1-5, 2021
• Paul Breiding
Technische Universität Berlin
Feb 3-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Michel Brion
Université Grenoble Alpes
Feb 1-May 8, 2021
• Jennifer Brown
UC Davis
Feb 1-5, 2021
• Jose Brox
Centre for Mathematics of the University of Coimbra
Feb 1-5, 2021; Feb 15-19, 2021
• Juliette Bruce
University of California, Berkeley / MSRI
Feb 1-May 7, 2021
• Laura Brustenga i Moncusi
University of Copenhagen
Feb 15-19, 2021
• Taylor Brysiewicz
Max Planck Institute for Mathematics in the Sciences
Feb 1-5, 2021; Feb 15-19, 2021
• Anders Buch
Rutgers University
Feb 1-May 8, 2021
• Daniel Bump
Stanford University
Feb 15-19, 2021
• Amanda Burcroff
Durham University
Feb 1-May 7, 2021
• Hannah Burson
University of Minnesota
Feb 1-5, 2021
• Mahir Bilen Can
Tulane University
Feb 1-May 7, 2021
• Erik Carlsson
UC Davis
Apr 7, 2021
• Federico Castillo
University of Kansas
Apr 12-16, 2021
• Federico Castillo
Max Planck Institute for Mathematics in the Sciences (MiS) in Leipzig.
Feb 1-5, 2021
• Eduardo Cattani
University of Massachusetts Amherst
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Renzo Cavalieri
Apr 12-16, 2021
• Ian Cavey
The Ohio State University
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Seth Chaiken
University at Albany
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Teressa Chambers
Brown University
Feb 1-5, 2021
• Melody Chan
Brown University
Feb 1-May 7, 2021
• Megan Chang-Lee
Brown University
Feb 1-5, 2021
• Pierre-Emmanuel Chaput
université de Lorraine
Feb 15-19, 2021
• Rajarshi Chatterjee
Kazi Nazrul University
Apr 12-16, 2021
• Anastasia Chavez
University of California, Davis
Feb 1-May 7, 2021
• Enrique Chávez Martínez
Apr 12-16, 2021
• Yifan Chen
UC Berkeley
Feb 3-5, 2021
• Chongyao Chen
Duke University
Feb 1-5, 2021
• Linda Chen
Swarthmore College
Feb 1-5, 2021; Mar 22-26, 2021; Mar 31-May 5, 2021; Apr 12-16, 2021
• Ke Chen
Nanjing University
Feb 1-5, 2021
• Sunita Chepuri
University of Michigan
Feb 1-May 31, 2021
• Man-Wai Cheung
Harvard University
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Daniel Corey
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Alvaro Cornejo
San Francisco State University
Apr 12-16, 2021
• Ethan Cotterill
Federal Fluminense University
Apr 12-16, 2021
• Steven Creech
Brown University
Feb 1-5, 2021
• María Angélica Cueto
Ohio State University
Feb 1-5, 2021; Feb 14-20, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Mark Curiel
University of Hawaii at Manoa
Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Xinle Dai
Harvard University
Feb 1-May 7, 2021
• Xinle Dai
University of Waterloo
Feb 24-May 5, 2021
• Chiara Damiolini
Rutgers University
Mar 22-26, 2021
• Alessandro Danelon
University of Technology Eindhove
Feb 1-5, 2021
• Hailong Dao
University of Kansas
Feb 1-5, 2021
• Quang Dao
University of Michigan
Mar 24-26, 2021
• Frances Dean
University of Washington
Feb 1-5, 2021
• Wolfram Decker
Technische Universität Kaiserslautern
Feb 15-19, 2021
• Colin Defant
Princeton University
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Graham Denham
University of Western Ontario
Apr 12-16, 2021
• Hamdi Dervodeli
Kyoto University
Feb 15-19, 2021
• Papri Dey
University of Missouri
Feb 15-May 7, 2021
• Alexander Diaz-Lopez
Villanova Universiry
Mar 22-26, 2021
• Hunter Dinkins
University of North Carolina-Chapel Hill
Feb 1-5, 2021
• Anton Dochtermann
Texas State University
Feb 3-5, 2021
• Galen Dorpalen-Barry
University of Minnesota
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Theo Douvropoulos
University of Massachusetts, Amherst
Feb 1-May 7, 2021
• Jan Draisma
Universität Bern
Feb 1-5, 2021
• Anne Dranowski
Feb 1-May 7, 2021
• Nicholas Early
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Holger Eble
TU Berlin
Feb 15-19, 2021
• Christian Eder
University of Kaiserslautern
Feb 15-19, 2021
• Griffin Edwards
Brown University
Feb 1-5, 2021
• Richard Ehrenborg
University of Kentucky
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Balazs Elek
Cornell University
Feb 3-5, 2021; Mar 3-May 5, 2021; Mar 22-26, 2021
• Ben Elias
University of Oregon
Mar 22-26, 2021
• Matthew Emerson
Brown University
Feb 1-5, 2021
• Laura Escobar
Washington University- St. Louis
Feb 1-May 7, 2021
• Alexander Esterov
National Research University Higher School of Economics
Feb 1-5, 2021
• Sen-Peng Eu
National Taiwan Normal University
Feb 1-5, 2021
• Christopher Eur
Stanford University
Feb 1-May 7, 2021
• Eleonore Faber
University of Leeds
Apr 12-16, 2021
• Lorenzo Fantini
Goethe University Frankfurt
Feb 1-5, 2021; Apr 12-16, 2021
• Jeová Farias Sales Rocha Neto
Brown university
Feb 1-5, 2021
• Matthew Faust
Texas A&M University
Feb 1-May 7, 2021
• Elisenda Feliu
University of Copenhagen
Feb 1-5, 2021; Apr 12-16, 2021
• Luis Ferroni
University of Bologna
Feb 2-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Claudia Fevola
Max Planck Institute for Mathematics in the Sciences (Leipzig)
Feb 1-5, 2021
• Claus Fieker
University of Kaiserslautern
Feb 15-19, 2021
• Tara Fife
Max Planck Institute for mathematics in the Sciences
Feb 1-5, 2021; Apr 12-16, 2021
• Alex Fink
Apr 12-16, 2021
• Sergey Fomin
University of Michigan
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Garrett Fowler
Virginia Tech
Feb 1-5, 2021
• Netanel Friedenberg
Yale University
Feb 1-May 31, 2021
• Carrie Frizzell
Kansas State University
Feb 1-5, 2021
• Anne Frühbis-Krüger
University of Oldenburg
Feb 15-19, 2021
• William Fulton
University of Michigan
Feb 1-May 7, 2021
MIT
Feb 1-May 7, 2021
• Christian Gaetz
MIT
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Pavel Galashin
University of California, Los Angeles
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Yibo Gao
Massachusetts Institute of Technology
Feb 1-5, 2021; Mar 22-26, 2021
• Shiliang Gao
University of Illinois at Urbana-Champaign
Feb 1-5, 2021; Mar 22-26, 2021
• Dichuan Gao
Brown University
Feb 1-5, 2021
• Samuel-Louis Gardiner
Queen Mary University of London
Feb 3-5, 2021
• Marina Garrote-López
Universitat Politècnica de Catalunya
Feb 15-19, 2021
• Jack Garzella
University of California, San Diego
Feb 15-19, 2021
• Alheydis Geiger
Eberhard Karls University Tübingen
Feb 15-19, 2021
• Deniz Genlik
The Ohio State University
Feb 1-5, 2021; Mar 22-26, 2021
• Angela Gibney
Rutgers University, New Brunswick
Mar 22-26, 2021
• Julius Giesler
University of Tuebingen
Apr 12-16, 2021
• Maria Gillespie
Mar 17-May 5, 2021
• Andrey Glubokov
Ave Maria University
Feb 1-5, 2021; Feb 15-19, 2021; Feb 24-May 6, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Rebecca Goldin
George Mason University
Feb 1-5, 2021; Apr 12-16, 2021
• Sergio Gómez
CINVESTAV
Feb 1-5, 2021; Apr 12-16, 2021
• José González
University of California, Riverside
Apr 12-16, 2021
• Vassily Gorbounov
Higher School of Economics, Russia
Mar 7-Apr 30, 2021
• Brent Gorbutt
George Mason University
Apr 12-16, 2021
• Elisa Gorla
University of Neuchatel
Feb 24-May 5, 2021; Apr 12-16, 2021
• Eugene Gorsky
UC Davis
Feb 1-May 7, 2021
• Torin Greenwood
North Dakota State University
Feb 1-5, 2021
• Sean Griffin
Brown University
Jan 27-May 31, 2021
• Sarah Griffith
Brown University
Feb 1-5, 2021; Apr 12-16, 2021
• Darij Grinberg
Drexel University
Feb 1-5, 2021; Feb 15-19, 2021
• Helen Grundman
Bryn Mawr College
Feb 1-5, 2021
• Samuel Grushevsky
Stony Brook University
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Aziz Burak Guelen
The Ohio State University
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Emily Gunawan
University of Oklahoma
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021
• Trevor Gunn
Georgia Institute of Technology
Feb 1-5, 2021; Apr 12-16, 2021
• Ajeeth Gunna
The University of Melbourne
Feb 1-5, 2021; Apr 12-16, 2021
Lomonosov Moscow State University
Feb 1-5, 2021
• Christian Haase
Freie Universität Berlin
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Marvin Hahn
Max Planck Institute for Mathematics in the Sciences
Feb 1-5, 2021
• Iva Halacheva
Northeastern University
Feb 3-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Zachary Hamaker
University of Florida
Feb 1-5, 2021
• Wesley Hamilton
University of North Carolina, Chapel Hill
Feb 1-5, 2021
• Sang Geun Han
KAIST
Feb 1-5, 2021
• Kangjin Han
Daegu-Gyeongbuk Institute of Sciences and Technology (DGIST)
Feb 1-May 7, 2021
MCMASTER UNIVERSITY
Feb 1-May 7, 2021
• Pamela E. Harris
Williams College
Mar 22-26, 2021; Apr 12-16, 2021
• Jonathan Hauenstein
University of Notre Dame
Feb 15-19, 2021
• Xiang He
Hebrew University
Feb 1-5, 2021
• Lauren Heller
University of California, Berkeley
Feb 1-5, 2021
• Paul Helminck
Swansea University
Apr 12-16, 2021
• Oskar Henriksson
University of Copenhagen
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Milena Hering
The University of Edinburgh
Feb 1-May 7, 2021
• María Herrero
University of Buenos Aires - CONICET
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Dylan Heuer
North Dakota State University
Feb 1-5, 2021
• Cvetelina Hill
Georgia Institute of Technology
Feb 2-5, 2021
• Joseph Hlavinka
Brown University
Feb 1-5, 2021
• Do Kien Hoang
Yale University
Feb 1-5, 2021
• Reuven Hodges
University of Illinois at Urbana-Champaign
Feb 1-5, 2021
• Tommy Hofmann
TU Kaiserslautern
Feb 15-19, 2021
• Roser Homs Pons
Technical University of Munich
Feb 1-5, 2021
• Neha Hooda
Fairfield University
Apr 12-16, 2021
• Eric Hopper
Duke University
Feb 1-5, 2021
• Max Horn
Technische Universität Kaiserslautern
Feb 15-19, 2021
• Serkan Hosten
San Francisco State University
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Daoji Huang
Brown University
Sep 1, 2020-May 31, 2021
• Yifeng Huang
University of Michigan
Feb 1-May 7, 2021
• Suzanne Huaringa Mosquera
PUCP
Feb 1-5, 2021
• June Huh
Stanford University
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Benjamin Hutz
Saint Louis University
Feb 15-19, 2021
• Brian Hwang
Cornell University
Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Anthony Iarrobino
Northeastern University
Feb 1-May 7, 2021
United Arab Emirates University
Apr 12-16, 2021
• Bogdan Ion
University of Pittsburgh
Feb 1-May 7, 2021
• Alexey Izmailov
Brown University
Feb 1-5, 2021; Feb 15-19, 2021
• Shashank Jaiswal
Purdue University
Apr 12-16, 2021
• Delio Jaramillo
Cinvestav-IPN (MEXICO)
Apr 12-16, 2021
• Manoel Jarra
IMPA
Feb 1-5, 2021; Apr 12-16, 2021
• David Jensen
University of Kentucky
Feb 1-May 7, 2021; Mar 3-May 5, 2021
• Minyoung Jeon
The Ohio State University
Mar 22-26, 2021; Apr 12-16, 2021
• Sam Jeralds
University of North Carolina at Chapel Hill
Feb 1-5, 2021; Mar 22-26, 2021
• Shuai Jiang
Virginia Tech
Feb 1-May 7, 2021
• Tong Jin
Georgia Institute of Technology
Apr 12-16, 2021
• Michael Joswig
TU Berlin & MPI Leipzig
Feb 1-May 7, 2021
• Nidhi Kaihnsa
Brown University
Feb 1-May 7, 2021
• Elana Kalashnikov
Harvard University
Feb 1-5, 2021; Apr 28, 2021
• Marek Kaluba
Technische Universität Berlin
Feb 15-19, 2021
• Siddarth Kannan
Brown University
Feb 1-May 7, 2021
• Daniel Kaplan
University of Birmingham
Feb 1-5, 2021
• Selvi Kara
University of South Alabama
Feb 1-5, 2021
• Lars Kastner
Institute of Mathematics of the Technical University
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Syu Kato
Kyoto University
Mar 17-May 7, 2021
• Eric Katz
The Ohio State University
Apr 12-16, 2021
• Kiumars Kaveh
University of Pittsburgh
Apr 12-16, 2021
• Kiran Kedlaya
University of California, San Diego
Feb 15-19, 2021
• Hannah Keese
Cornell University
Mar 3-May 5, 2021; Mar 22-26, 2021
• Elizabeth Kelley
University of MInnesota
Feb 1-5, 2021; Apr 12-16, 2021
• Gary Kennedy
Ohio State University
Feb 1-May 7, 2021
• Nguyen Khanh
Institut Camille Jordan
Feb 1-5, 2021; Feb 15-19, 2021; Mar 3-May 5, 2021; Apr 12-16, 2021
• Joshua Kiers
Ohio State University
Feb 1-5, 2021; Mar 22-26, 2021
• Shinyoung Kim
Institute for Basic Science Center for Geometry and Physics
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Young Rock Kim
Hankuk University of Foreign Studies
Mar 22-26, 2021; Apr 12-16, 2021
• Donghyun Kim
UC Berkeley
Feb 1-5, 2021
• Jaehyung Kim
University of Illinois - Urbana Champaign
Feb 1-5, 2021
• Patricia Klein
University of Minnesota
Feb 1-May 7, 2021
• Allen Knutson
Cornell University
Feb 1-5, 2021; Feb 15-May 7, 2021
• Kathlén Kohn
KTH Royal Institute of Technology
Apr 12-16, 2021
• Aleksandr Kolpakov
University of Neuchâtel
Mar 22-26, 2021; Apr 12-16, 2021
• Jakub Koncki
Institute of Mathematics, Polish Academy of Sciences
Feb 1-May 7, 2021
• Matthias Köppe
UC Davis
Feb 15-19, 2021
• Korkeat Korkeathikhun
University of North Carolina at Chapel Hill
Feb 1-5, 2021; Mar 22-26, 2021
• Gaurish Korpal
University of Arizona
Feb 15-19, 2021
• Lukas Kühne
Max Planck Institute for Mathematics in the Sciences
Feb 1-May 7, 2021
• Tri Lai
Feb 1-5, 2021
• Pierre Lairez
INRIA
Feb 15-19, 2021
• Thomas Lam
University of Michigan
Feb 1-May 7, 2021
• Tyler Lane
Brown University
Feb 1-5, 2021
• Matthew Larson
Stanford University
Feb 1-May 7, 2021
• Cédric Le Texier
Universitetet i Oslo
Apr 12-16, 2021
• Kang-Ju Lee
Seoul National University
Feb 1-5, 2021; Feb 24-May 5, 2021
• Eunjeong Lee
IBS-CGP
Apr 12-16, 2021
• Samuel Lelièvre
Université Paris-Saclay
Feb 15-19, 2021
• Yoav Len
University of St Andrews
Feb 1-5, 2021; Apr 12-16, 2021
• Cristian Lenart
University at Albany
Feb 1-5, 2021; Mar 22-26, 2021
• Anton Leykin
Georgia Tech
Feb 15-19, 2021
• Chen Li
Brown University
Feb 1-5, 2021
• Shiyue Li
Brown University
Feb 1-May 7, 2021
• Daniel Li
Brown University
Feb 1-5, 2021
• Amy Li
University of Texas at Austin
Feb 3-5, 2021
• Yen-Kheng Lim
Xiamen University Malaysia
Apr 12-16, 2021
• Kuei-Nuan Lin
Penn State University, Greater Allegheny
Feb 1-5, 2021; Mar 22-26, 2021
• Feiyang Lin
Harvey Mudd College
Feb 1-5, 2021
• Davis Lister
Brown University
Feb 1-5, 2021
• Bingyan Liu
university of illinois (UIUC)
Feb 1-5, 2021
• Yuqing Liu
University of Michigan
Feb 1-5, 2021
• David Lowry-Duda
ICERM & Brown University
Feb 1-May 7, 2021
• Yuze Luan
UC Davis
Feb 1-5, 2021
• Trent Lucas
Brown University
Feb 1-5, 2021
• Antonio Macchia
Freie Universität Berlin
Feb 1-May 7, 2021
• Diane Maclagan
University of Warwick
Apr 12-16, 2021
• Timothy Magee
University of Birmingham
Feb 1-5, 2021; Apr 12-16, 2021
• Saikat Maity
University of Calcutta
Apr 12-16, 2021
• Firdous Mala
GDC Sopore, Bla
Feb 1-5, 2021
• Aimeric Malter
University of Birmingham
Feb 3-5, 2021
• Kelly Maluccio
Texas A&M University
Feb 15-19, 2021
• Travis Mandel
University of Oklahoma
Apr 12-16, 2021
• Yelena Mandelshtam
University of California, Berkeley
Feb 1-5, 2021
• Olya Mandelshtam
University of Waterloo
Mar 10-May 5, 2021
INDIAN INSTITUTE OF TECHNOLOGY BOMBAY
Feb 1-May 7, 2021
• Hannah Markwig
Eberhard Karls University of Tübingen
Feb 1-May 7, 2021
• Jesus Martinez-Garcia
University of Essex
Feb 1-5, 2021; Feb 15-19, 2021
• Lily Mayo
Brown University
Feb 1-5, 2021
• Mikhail Mazin
Kansas State University
Feb 1-May 7, 2021
• Jason McCullough
Iowa State University
Apr 12-16, 2021
• Alex McDonough
Brown University
Feb 1-May 7, 2021
• Jodi McWhirter
Washington University in St. Louis
Apr 12-16, 2021
• Hana Melánová
University of Vienna
Feb 15-19, 2021
• Margarida Melo
Universita Roma Tre
Feb 1-5, 2021
• Karola Meszaros
Cornell University
Apr 12-16, 2021
• Mike Michailidis
The MathWorks Inc.
Mar 22-26, 2021
• Leonardo Mihalcea
Virginia Polytechnic Institute and State University
Feb 1-May 7, 2021
• Elizabeth Milićević
Haverford College
Mar 3-May 5, 2021; Mar 15-Apr 16, 2021; Mar 22-26, 2021
• Kalina Mincheva
Yale University
Feb 15-19, 2021; Apr 12-16, 2021
• Luca Moci
Universita' di Bologna
Feb 1-5, 2021
Purdue University
Feb 1-5, 2021; Apr 12-16, 2021
University of Bristol
Feb 24-May 5, 2021
Ghent University
Feb 1-May 7, 2021
• Jonathan Montaño
New Mexico State University
Feb 1-5, 2021; Apr 12-16, 2021
• Héctor Montiel
UNAM
Feb 3-5, 2021; Apr 12-16, 2021
• Han-Bom Moon
Fordham University
Feb 1-5, 2021
• Alejandro Morales
University of Massachusetts, Amherst
Feb 1-5, 2021; Apr 12-16, 2021
• Sophie Morel
CNRS/ENS Lyon
Feb 3-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Marc Moreno
University of Western Ontario
Feb 15-19, 2021
• Ralph Morrison
Williams College
Feb 1-5, 2021; Apr 12-16, 2021
• Jennifer Morse
University of Virginia
Feb 1-5, 2021; Feb 15-19, 2021; Mar 21-27, 2021; Apr 12-16, 2021
• Chenqi Mou
Beihang University, China
Mar 22-26, 2021
• Hanna Mularczyk
Harvard University
Feb 3-5, 2021
• Tommi Muller
University Of British Columbia
Apr 12-16, 2021
• Reshma Munbodh
Alpert Medical School of Brown University
Apr 12-16, 2021
• Gregg Musiker
University of Minnesota
Feb 1-5, 2021
• Robert Muth
Washington & Jefferson College
Mar 22-26, 2021
Institut Camille Jordan
Feb 1-5, 2021; Feb 15-19, 2021; Feb 24-May 5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Uwe Nagel
University of Kentucky
Feb 1-5, 2021
• Alfredo Nájera Chávez
Mathematics Institute UNAM, Oaxaca
Apr 12-16, 2021
• Hiroshi Naruse
University of Yamanashi
Feb 1-May 7, 2021
• Evangelos Nastas
SUNY
Feb 15-19, 2021
• Abhiram Natarajan
Purdue University
Feb 3-5, 2021
• Benjamin Nativi
The University of Texas at Austin
Feb 3-5, 2021; Apr 12-16, 2021
• Gleb Nenashev
Brown University
Feb 1-May 31, 2021
• Xianglong Ni
University of California, Berkeley
Feb 1-5, 2021
• Nathan Nichols
University Of Minnesota Twin Cities
Feb 1-5, 2021
• Ivan Nikitin
NRU HSE
Feb 1-5, 2021
• Benjamin Nill
University of Magdeburg
Apr 12-16, 2021
• Mounir Nisse
Xiamen University Malaysia
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Augustine O'Keefe
Connecticut College
Feb 1-5, 2021
• Damián Ochoa
Apr 12-16, 2021
• David Oetjen
Virginia Tech
Feb 1-5, 2021; Mar 3-May 5, 2021; Mar 22-26, 2021
• Jaeseong Oh
Seoul National University
Feb 1-5, 2021
• Gidon Orelowitz
University of Illinois, Urbana-Champaign
Feb 1-5, 2021
• Daniel Orr
Virginia Tech
Mar 22-26, 2021; Mar 31-May 5, 2021
• Alperen Ozdemir
Georgia Tech
Feb 1-5, 2021
• Roberto Pagaria
Alma Mater Studiorum Università di Bologna
Feb 1-5, 2021; Feb 15-19, 2021
• Jianping Pan
University of California, Davis
Feb 1-May 7, 2021
• Marta Panizzut
TU Berlin
Feb 1-5, 2021; Feb 15-19, 2021
• Theodoros Stylianos Papazachariou
University of Essex
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Joseph Pappe
UC Davis
Feb 1-5, 2021
• Matteo Parisi
University of Oxford
Feb 3-5, 2021; Apr 12-16, 2021
• Beatriz Pascual Escudero
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Brendan Pawlowski
University of Southern California
Feb 1-5, 2021; Mar 22-26, 2021
• Sam Payne
University of Texas at Austin
Jan 31-May 8, 2021
• Oliver Pechenik
University of Michigan
Feb 1-5, 2021; Mar 22-26, 2021
• Raul Penaguiao
San Francisco State University
Feb 2-5, 2021
• Michael Perlman
Queen's University
Mar 22-26, 2021
• Nicolas Perrin
Versailles Saint-Quentin-en-Yvelines University
Feb 1-May 7, 2021
• Nathan Pflueger
Amherst College
Feb 1-May 7, 2021
• Viviane Pons
Université Paris Sud
Feb 15-19, 2021
• Irem Portakal
Otto-von-Guericke-Universitaet Magdeburg
Feb 15-19, 2021; Apr 12-16, 2021
• Martha Precup
Washington University in St. Louis
Mar 22-26, 2021
• Ying Anna Pun
University of Virginia
Feb 1-5, 2021; Mar 22-26, 2021
• Jiayue Qi
University of Linz
Feb 1-5, 2021
• Zhijun (George) Qiao
University of Texas Rio Grande Valley
Apr 12-16, 2021; Apr 21-May 5, 2021
• Jenna Rajchgot
McMaster University
Mar 22-26, 2021; Apr 12-16, 2021
Brown University
Feb 1-5, 2021; Feb 24-May 5, 2021; Apr 12-16, 2021
• Arvind Ramaswami
Georgia Institute of Technology
Feb 1-5, 2021
• Alondra Ramírez Sandoval
Apr 12-16, 2021
• Dhruv Ranganathan
University of Cambridge
Apr 12-16, 2021
University of Kentucky
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Yue Ren
Swansea University
Apr 12-16, 2021
• William Reynolds
University of Edinburgh
Feb 1-5, 2021; Apr 12-16, 2021
University of California, San Diego
Feb 1-5, 2021
• Harry Richman
University of Washington
Apr 12-16, 2021
• Edward Richmond
Oklahoma State University
Feb 1-5, 2021; Mar 30-May 5, 2021
• Konstanze Rietsch
King's College London
Feb 1-May 7, 2021
• Richard Rimanyi
University of North Carolina at Chapel Hill
Feb 1-5, 2021; Mar 3-May 5, 2021; Mar 22-26, 2021
• Jesus Rivera Ramirez
CINVESTAV
Feb 1-5, 2021
• Diego Robayo Bargans
Feb 1-5, 2021
• Colleen Robichaux
University of Illinois at Urbana-Champaign
Feb 1-May 7, 2021
• Colleen Robles
Duke University
Feb 1-5, 2021
• Alejandro Rodriguez Matta
Apr 12-16, 2021
• David Roe
Massachusetts Institute of Technology
Feb 15-19, 2021
• Felix Röhrle
Goethe University Frankfurt
Feb 1-5, 2021; Apr 12-16, 2021
• Piotr Rudnicki
University of Warsaw
Feb 1-5, 2021
• Oliver Ruff
Kent State University
Mar 22-26, 2021
• Julian Rüth
none
Feb 15-19, 2021
• Felix Rydell
KTH
Apr 12-16, 2021
• María Sabando Alvarez
Washington University in St. Louis
Apr 12-16, 2021
Bates College
Feb 15-19, 2021
• Francisco Santos
University of Cantabria
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Anna-Laura Sattelberger
Max Planck Institute for Mathematics in the Sciences
Feb 15-19, 2021
• Justin Sawon
University of North Carolina - Chapel Hill
Feb 1-5, 2021
• Mahrud Sayrafi
University of Minnesota
Feb 1-May 7, 2021
• Hal Schenck
Auburn University
Feb 1-May 7, 2021
• Hal Schenck
Iowa State University
Feb 24-May 5, 2021
• Anne Schilling
UC Davis
Feb 1-5, 2021; Feb 15-19, 2021; Mar 24-26, 2021
• Bernd Schober
Carl von Ossietzky Universität Oldenburg
Apr 12-16, 2021
• Nolan Schock
University of Georgia
Apr 12-16, 2021
• Georgy Scholten
North Carolina State University
Feb 3-5, 2021
• Daniel Schultz
Technische Universität Kaiserslautern
Feb 15-19, 2021
State University of New York, University at Albany
Feb 3-5, 2021
• Alexandra Seceleanu
Apr 12-16, 2021
• George Seelinger
University of Virginia
Feb 1-5, 2021; Mar 22-26, 2021
• Maiko Serizawa
University of Ottawa
Mar 31-May 5, 2021
• Stefano Serpente
Università degli Studi Roma 3
Feb 1-5, 2021
• Oswaldo Sevilla
Centro de Investigación en Matemáticas, Guanajuato Mexico
Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Tim Seynnaeve
University of Bern
Feb 1-5, 2021
• Aniket Shah
The Ohio State University
Feb 3-5, 2021; Apr 12-16, 2021
• Kristin Shaw
University of Oslo
Feb 1-5, 2021; Apr 12-16, 2021
• Melissa Sherman-Bennett
UC Berkeley/Harvard
Feb 1-May 7, 2021; Mar 3-May 5, 2021
• Ryan Shifler
Salisbury University
Feb 1-5, 2021; Feb 24-May 5, 2021
• Mark Shimozono
Virginia Tech
Feb 1-5, 2021; Mar 21-27, 2021
• Farbod Shokrieh
University of Washington
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Yiyan Shou
UNC - Chapel Hill
Feb 1-5, 2021; Apr 22, 2021
• Kevin Shu
Georgia Institute of Technology
Apr 12-16, 2021
• Eugenii Shustin
Tel Aviv University
Apr 12-16, 2021
• Sergio Silva
Universidad Distrital Francisco Jose de Caldas
Apr 12-16, 2021
• Rob Silversmith
Northeastern University
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Jose Simental Rodriguez
Max-Planck Institute for Mathematics
Mar 22-26, 2021
• Connor Simpson
Feb 1-May 7, 2021
• Rahul Singh
Virginia Polytechnic Institute and State University
Feb 1-5, 2021; Feb 24-May 5, 2021
• Uriel Sinichkin
Tel Aviv University
Feb 1-5, 2021; Apr 12-16, 2021
• Gregory Smith
Queen's University
Apr 12-16, 2021
• Jason Snyder
University of California, Los Angeles
Feb 3-5, 2021
• Ivan So
Michigan State University
Apr 12-16, 2021
• Eric Sommers
University of Massachusetts
Mar 22-26, 2021
• Miruna-Stefana Sorea
SISSA, Trieste
Feb 1-May 7, 2021
• Frank Sottile
Texas A&M University
Feb 1-5, 2021; Feb 14-20, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Pedro Souza
Goethe Universität Frankfurt am Main
Feb 1-5, 2021; Apr 12-16, 2021
• David Speyer
University of Michigan
Feb 1-5, 2021; Apr 11-17, 2021
• Sylvain Spitz
TU Berlin
Feb 15-19, 2021
• Avery St. Dizier
Univeristy of Illinois at Urbana-Champaign
Feb 1-May 7, 2021
• Evgeny Statnik
Higher School of Economics
Feb 1-5, 2021
• Jessica Striker
North Dakota State University
Feb 1-5, 2021; Mar 22-26, 2021
• Eric Stucky
University of Minnesota-Twin Cities
Feb 1-5, 2021; Feb 24-May 5, 2021
• Bernd Sturmfels
MPI Leipzig
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Changjian Su
University of Toronto
Feb 1-5, 2021; Feb 15-19, 2021; Mar 3-May 5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Nawaz Sultani
University of Michigan
Feb 1-5, 2021; Feb 15-19, 2021
• Yuri Sulyma
Brown University
Feb 1-May 7, 2021
• Kevin Summers
Virginia Polytechnic Institute and State University
Feb 1-5, 2021
• Mariel Supina
University of California, Berkeley
Feb 1-May 7, 2021
• Joshua Swanson
University of California, San Diego
Mar 22-26, 2021
• Nafie Tairi
University of Bern
Feb 1-5, 2021
• Henry Talbott
Brown University
Feb 1-5, 2021
• Pedro Tamaroff
Trinity College Dublin
Feb 15-19, 2021
• Daniel Tamayo Jiménez
Université Paris-Saclay
Mar 22-26, 2021
• Anna Tao
Brown University
Feb 1-May 7, 2021
• Nicola Tarasca
Virginia Commonwealth University
Feb 1-May 7, 2021
• Mojdeh Tarighat
University of Virginia
Mar 22-26, 2021
Rutgers University
Feb 1-5, 2021; Mar 3-May 5, 2021
• Andrew Tawfeek
Amherst College
Feb 1-5, 2021; Apr 21-May 5, 2021
• Máté Telek
University of Copenhagen
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Ayush Tewari
TU Berlin
Feb 1-May 7, 2021
• Ayush Tewari
Eberhard Karls Universitat Tubingen
Feb 24-May 5, 2021
• Vasu Tewari
University of Hawaii
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Warut Thawinrak
University of California Davis
Feb 1-5, 2021
• Nicolas Thiéry
Université Paris Sud
Feb 15-19, 2021
• Zonglin Tian
Texas A & M University
Feb 1-5, 2021
• Angelica Torres
KTH Royal Institute of Technology
Feb 1-5, 2021
• Joaquin Torres Henestroza
Universidad Nacional Autónoma de México, UNAM
Apr 12-16, 2021
• Trang Tran
Ucsc
Feb 1-5, 2021; Apr 12-16, 2021
Sandia National Laboratory
Feb 1-5, 2021
• Ling Hei Tsang
The Ohio State University
Feb 1-5, 2021; Feb 15-19, 2021; Apr 12-16, 2021
• Daniele Turchetti
Durham University
Feb 1-5, 2021
• Martin Ulirsch
Goethe University Frankfurt
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Jeremy Usatine
Brown University
Feb 1-May 7, 2021
• Ravi Vakil
Stanford University
Feb 1-May 7, 2021
• Bart Van Steirteghem
CUNY and FAU Erlangen-Nuernberg
Apr 12-16, 2021
• Alejandro Vargas
University of Bern
Feb 1-5, 2021
• Paul Vater
Max Planck Institute for Mathematics in the Sciences
Feb 15-19, 2021
• Lorenzo Vecchi
Alma Mater Studiorum - Università di Bologna
Feb 1-5, 2021; Feb 15-19, 2021; Feb 24-May 5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Emanuele Ventura
University of Bern
Feb 1-May 7, 2021
• Diego Villamizar
Tulane University
Mar 22-26, 2021
• Filippo Viviani
Roma Tre University
Feb 1-5, 2021
• Duc Vo
Harvard University
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Arina Voorhaar
Université de Genève
Feb 1-5, 2021
• Daniel Wang
Brown University
Feb 1-5, 2021
• Chengyang Wang
UC Davis
Feb 1-5, 2021
• Jeremy Wang
Brown University
Feb 1-5, 2021
• Charles Wang
Harvard University
Feb 1-5, 2021
• Ying Wang
Feb 1-5, 2021
• Weikun Wang
Southern University of Science and Technology
Feb 1-5, 2021; Feb 15-19, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Jidong Wang
University of Oregon
Feb 3-5, 2021
• Andrzej Weber
Uniwersity of Warsaw
Feb 1-May 7, 2021
• Ivy Wei
University of Minnesota
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Anna Weigandt
University of Michigan
Feb 1-May 7, 2021; Mar 22-26, 2021
• Max Weinreich
Brown University
Feb 1-5, 2021
• Nathaniel Welty
Texas A&M University
Feb 1-5, 2021
• Daping Weng
Michigan State University
Apr 12-16, 2021
Swarthmore College
Mar 22-26, 2021
• Rebecca Whitman
UC Berkeley
Feb 1-5, 2021
• Amy Wiebe
Freie Universität Berlin
Feb 1-5, 2021
• Harold Williams
University of Southern California
Mar 22-26, 2021
• Lauren Williams
Harvard University
Feb 1-May 7, 2021
• Kaelyn Willingham
The Ohio State University
Feb 3-5, 2021; Apr 12-16, 2021
• Rosa Winter
Max Planck Institute for Mathematics in the Sciences, Leipzig
Feb 15-19, 2021
• Camron Withrow
Virginia Tech
Feb 1-5, 2021
• Corey Wolfe
Tulane University
Feb 1-May 7, 2021
• Tian An Wong
University of Michigan-Dearborn
Mar 22-26, 2021
• Russ Woodroofe
University of Primorska
Feb 1-5, 2021
• Cameron Wright
University of Washington
Feb 1-May 7, 2021
• Kayla Wright
University of Minnesota
Feb 1-5, 2021
• Chenxi Wu
Feb 1-5, 2021
• Ralph Xu
Syracuse University
Feb 15-19, 2021
• Weihong Xu
Rutgers
Feb 1-May 7, 2021
• Damir Yeliussizov
Kazakh-British Technical University
Feb 1-May 7, 2021
• Alexander Yong
University of Illinois at Urbana-Champaign
Feb 1-May 7, 2021
• Semin Yoo
University of Rochester
Feb 1-5, 2021; Feb 24-May 5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Benjamin Young
University of Oregon
Feb 15-19, 2021
• Tianyi Yu
University of California, San Diego
Feb 1-5, 2021
• Josephine Yu
Georgia Institute of Technology
Feb 1-5, 2021
• Chi Ho Yuen
Brown University
Feb 1-May 7, 2021
• Claudia Yun
Brown University
Feb 1-May 7, 2021
• Oguzhan Yürük
TU Berlin
Feb 15-19, 2021
• Dmitry Zakharov
Central Michigan University
Feb 1-5, 2021; Apr 12-16, 2021
Amirkabir University of Technology
Apr 12-16, 2021
• Yuanning Zhang
UC Berkeley
Feb 1-5, 2021; Apr 12-16, 2021
• Xiping Zhang
Fudan University
Feb 1-5, 2021
• Zehong Zhao
University of California, San Diego
Feb 1-5, 2021
• Changlong Zhong
State University of New York Albany
Feb 1-5, 2021; Mar 22-26, 2021; Apr 12-16, 2021
• Xu Zhuang
Jilin University
Feb 1-5, 2021
• Paul Zinn-Justin
The University of Melbourne
Feb 1-May 7, 2021

Visit dates listed on the participant list may be tentative and subject to change without notice.

#### Semester Schedule

##### Monday, February 1, 2021
###### VIRTUAL ONLY: Introductory Workshop: Combinatorial Algebraic Geometry
• 9:50 - 10:00 am EST
Welcome
Virtual
• Brendan Hassett, ICERM/Brown University
• 10:00 - 10:45 am EST
Short Introduction to Hodge Structures Part 1
Virtual
• Colleen Robles, Duke University
###### Abstract
I will introduce Hodge structures and describe the linear structures underlying the Hard Lefschetz Theorem and Hodge--Riemann Bilinear Relations.
• 11:00 am - 12:00 pm EST
Problem Session 1
Problem Session - Virtual
• 12:00 - 12:30 pm EST
Short Introduction to Hodge Structures Part 2
Virtual
• Colleen Robles, Duke University
###### Abstract
I will introduce Hodge structures and describe the linear structures underlying the Hard Lefschetz Theorem and Hodge--Riemann Bilinear Relations.
• 12:30 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 2:45 pm EST
Basic Schubert Calculus Part 1
Virtual
• Sara Billey, University of Washington
• 3:00 - 4:00 pm EST
Problem Session 2
Problem Session - Virtual
• 4:00 - 4:30 pm EST
Basic Schubert Calculus Part 2
Virtual
• Sara Billey, University of Washington
• 4:30 - 5:15 pm EST
Reception
Virtual
##### Tuesday, February 2, 2021
###### VIRTUAL ONLY: Introductory Workshop: Combinatorial Algebraic Geometry
• 9:00 - 9:45 am EST
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:45 am EST
Basic notions in cotangent Schubert calculus - Part 1
Virtual
• Richard Rimanyi, University of North Carolina at Chapel Hill
###### Abstract
A key notion of Schubert Calculus is the cohomology ring of a homogeneous space, together with a distinguished basis: the collection of Schubert classes. There is a one-parameter deformation of the notion "Schubert class", called Chern-Schwartz-MacPherson (CSM-) class (a.k.a. characteristic cycle class, or cohomological stable envelope). In this lecture/workshop we will define the CSM class, and illustrate many of its properties through examples.
• 11:00 am - 12:00 pm EST
Problem Session 3
Problem Session - Virtual
• 12:00 - 12:30 pm EST
Basic notions in cotangent Schubert calculus - Part 2
Virtual
• Richard Rimanyi, University of North Carolina at Chapel Hill
###### Abstract
A key notion of Schubert Calculus is the cohomology ring of a homogeneous space, together with a distinguished basis: the collection of Schubert classes. There is a one-parameter deformation of the notion "Schubert class", called Chern-Schwartz-MacPherson (CSM-) class (a.k.a. characteristic cycle class, or cohomological stable envelope). In this lecture/workshop we will define the CSM class, and illustrate many of its properties through examples.
• 12:30 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 2:45 pm EST
Matroids Part 1
Virtual
• Christopher Eur, Stanford University
###### Abstract
We give an introduction to matroid theory with a view towards its recent interactions with algebraic geometry. In the first half, we study matroids as combinatorial abstractions of hyperplane arrangements, which will lead us to Chow rings of matroids, modeled after the geometry of wonderful compactifications of hyperplane arrangement complements. In the second half, we give a broad survey of some recent developments involving other different but related algebro-geometric models of matroids.
• 3:00 - 4:00 pm EST
Problem Session 4
Problem Session - Virtual
• 4:00 - 4:30 pm EST
Matroids Part 2
Virtual
• Christopher Eur, Stanford University
###### Abstract
We give an introduction to matroid theory with a view towards its recent interactions with algebraic geometry. In the first half, we study matroids as combinatorial abstractions of hyperplane arrangements, which will lead us to Chow rings of matroids, modeled after the geometry of wonderful compactifications of hyperplane arrangement complements. In the second half, we give a broad survey of some recent developments involving other different but related algebro-geometric models of matroids.
##### Wednesday, February 3, 2021
###### VIRTUAL ONLY: Introductory Workshop: Combinatorial Algebraic Geometry
• 10:00 - 10:45 am EST
Quantum Cohomology Part 1
Virtual
• Nicolas Perrin, Versailles Saint-Quentin-en-Yvelines University
• 11:00 am - 12:00 pm EST
Problem Session 5
Problem Session - Virtual
• 12:00 - 12:30 pm EST
Quantum Cohomology Part 2
Virtual
• Nicolas Perrin, Versailles Saint-Quentin-en-Yvelines University
• 12:30 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 2:45 pm EST
Affine Schubert Calculus Part 1
Virtual
• Mark Shimozono, Virginia Tech
• 3:00 - 4:00 pm EST
Problem Session 6
Problem Session - Virtual
• 4:00 - 4:30 pm EST
Affine Schubert Calculus Part 2
Virtual
• Mark Shimozono, Virginia Tech
• 4:30 - 5:15 pm EST
Gathertown Afternoon Coffee - Informal Grad Student / Postdoc Focused
Coffee Break - Virtual
##### Thursday, February 4, 2021
###### VIRTUAL ONLY: Introductory Workshop: Combinatorial Algebraic Geometry
• 9:00 - 9:45 am EST
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:45 am EST
Introduction to Tropical Geometry Through Curves - Part 1
Virtual
###### Abstract
Tropical geometry equips varieties with a combinatorial counterpart called the tropicalization. In this talk, I will introduce some of the key ideas in tropical geometry by studying curves. This will include definitions and examples of embedded tropicalization for curves in the plane, abstract tropicalization / dual graphs, and Berkovich skeleta.
• 11:00 am - 12:00 pm EST
Problem Session 7
Problem Session - Virtual
• 12:00 - 12:30 pm EST
Introduction to Tropical Geometry Through Curves - Part 2
Virtual
###### Abstract
Tropical geometry equips varieties with a combinatorial counterpart called the tropicalization. In this talk, I will introduce some of the key ideas in tropical geometry by studying curves. This will include definitions and examples of embedded tropicalization for curves in the plane, abstract tropicalization / dual graphs, and Berkovich skeleta.
• 12:30 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 2:45 pm EST
Moduli spaces of tropical curves Part 1
Virtual
• Sam Payne, University of Texas at Austin
###### Abstract
In the first part of this talk, I will introduce the moduli space of stable tropical curves and discuss its combinatorial structure and topology, illustrating with simple examples in low genus. In the problem session, you will compute one further example. And in the second half of the talk, I will explain some general results about the topology of moduli spaces of stable tropical curves, how these relate to the topology of the algebraic moduli spaces M_g and M_{g,n}, and then state some open problems and conjectures that you may find interesting to think about during the semester.
• 3:00 - 4:00 pm EST
Problem Session 8
Problem Session - Virtual
• 4:00 - 4:30 pm EST
Moduli spaces of tropical curves Part 2
Virtual
• Sam Payne, University of Texas at Austin
###### Abstract
In the first part of this talk, I will introduce the moduli space of stable tropical curves and discuss its combinatorial structure and topology, illustrating with simple examples in low genus. In the problem session, you will compute one further example. And in the second half of the talk, I will explain some general results about the topology of moduli spaces of stable tropical curves, how these relate to the topology of the algebraic moduli spaces M_g and M_{g,n}, and then state some open problems and conjectures that you may find interesting to think about during the semester.
##### Friday, February 5, 2021
###### VIRTUAL ONLY: Introductory Workshop: Combinatorial Algebraic Geometry
• 10:00 - 10:45 am EST
Cluster structures in commutative rings Part 1
Virtual
• Lauren Williams, Harvard University
###### Abstract
In my first talk, I will give a gentle introduction to cluster algebras. In the second talk, I will describe how to identify a commutative ring (such as the coordinate ring of an algebraic variety) with a cluster algebra, and provide several examples. I will also discuss how to describe cluster algebras by generators and relations.
• 11:00 am - 12:00 pm EST
Problem Session 9
Problem Session - Virtual
• 12:00 - 12:30 pm EST
Cluster structures in commutative rings Part 2
Virtual
• Lauren Williams, Harvard University
###### Abstract
In my first talk, I will give a gentle introduction to cluster algebras. In the second talk, I will describe how to identify a commutative ring (such as the coordinate ring of an algebraic variety) with a cluster algebra, and provide several examples. I will also discuss how to describe cluster algebras by generators and relations.
• 12:30 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 2:45 pm EST
Cluster varieties Part 1
Virtual
• David Speyer, University of Michigan
###### Abstract
We will discuss the geometry of the affine algebraic varieties associated to cluster algebras. In the first hour, we will give examples and talk about open sets, smoothness and covering maps; in the second hour, we will talk about mixed Hodge structures.
• 3:00 - 4:00 pm EST
Problem Session 10
Problem Session - Virtual
• 4:00 - 4:45 pm EST
Cluster varieties Part 2
Virtual
• David Speyer, University of Michigan
###### Abstract
We will discuss the geometry of the affine algebraic varieties associated to cluster algebras. In the first hour, we will give examples and talk about open sets, smoothness and covering maps; in the second hour, we will talk about mixed Hodge structures.
##### Monday, February 8, 2021
###### Combinatorial Algebraic Geometry
• 11:00 - 11:30 am EST
Welcome to ICERM
Welcome - Virtual
• Brendan Hassett, ICERM/Brown University
• 1:30 - 2:00 pm EST
Organizer / Directorate Meeting
Meeting - Virtual
##### Tuesday, February 9, 2021
###### Combinatorial Algebraic Geometry
• 2:30 - 3:50 pm EST
Virtual
• Jeremy Usatine, Brown University
##### Wednesday, February 10, 2021
###### Combinatorial Algebraic Geometry
• 11:00 am - 12:00 pm EST
Meeting - Virtual
• 3:30 - 4:30 pm EST
Degeneracy Loci and Schubert Polynomials
Virtual
• William Fulton, University of Michigan
###### Abstract
This talk emphasizes how finding formulae for degeneracy loci leads naturally to the algebra of Schubert polynomials. We'll see how this illuminates the study of Schubert polynomials in the 19th, 20th, and 21st century. (Joint work with Dave Anderson.)
##### Thursday, February 11, 2021
###### Combinatorial Algebraic Geometry
• 2:30 - 3:50 pm EST
Virtual
• Jeremy Usatine, Brown University
• 4:30 - 5:15 pm EST
Hodge-Riemann relations and Lorentzian polynomials
Virtual
• Christopher Eur, Stanford University
###### Abstract
We introduce the theory of Lorentzian polynomials, motivated by the Hodge-Riemann relations and the resulting properties that cohomology rings of smooth complex projective varieties satisfy.
##### Friday, February 12, 2021
###### Combinatorial Algebraic Geometry
• 10:30 - 11:30 am EST
Virtual
• 11:30 am - 12:00 pm EST
Graduate Student/postdoc post-seminar break in Gather
Coffee Break - Virtual
• 4:30 - 5:00 pm EST
Hodge-Riemann relations and Lorentzian polynomials cont.
Virtual
• Christopher Eur, Stanford University
###### Abstract
We introduce the theory of Lorentzian polynomials, motivated by the Hodge-Riemann relations and the resulting properties that cohomology rings of smooth complex projective varieties satisfy.
##### Monday, February 15, 2021
###### VIRTUAL ONLY: Sage/Oscar Days for Combinatorial Algebraic Geometry
• 9:45 - 10:00 am EST
Welcome
Virtual
• Brendan Hassett, ICERM/Brown University
• 10:00 - 10:30 am EST
A brief tour of Sage
Virtual
• Nicolas Thiéry, Université Paris Sud
###### Abstract
I will offer a brief tour of Sage, showcasing some features and use cases, hinting at its development model, pointing to some recent trends, and highlighting how it fits within the larger ecosystem of free computational (mathematics) software.
• 10:45 - 11:15 am EST
Rings and fields in Sage
Virtual
• David Roe, Massachusetts Institute of Technology
###### Abstract
I will give an introduction to basic algebraic structures in Sage, with a focus on the coercion model, finite fields and extensions of rings. I will also give an overview of how you can contribute to Sage.
• 11:15 - 11:30 am EST
Coffee Break
Virtual
• 11:30 am - 12:00 pm EST
Celestial mechanics via tropical geometry (gfan and Macaulay2)
Virtual
• Anton Leykin, Georgia Tech
• 12:15 - 12:45 pm EST
FusionRings in Sage 9.2
Virtual
• Daniel Bump, Stanford University
###### Abstract
The FusionRing class implements useful methods for Verlinde Algebras. These are elegant rings similar to WeylCharacterRings (representation rings of Lie groups) except that the fusion categories have only finitely many objects. These rings have applications to conformal field theory, quantum groups, topological quantum computing and knot theory. Most of the methods needed to work with these have been implemented in Sage 9.2. We will review the math and show what the code can do. The FusionRing code is joint work with Guillermo Aboumrad.
• 1:00 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 3:00 pm EST
Gathertown Welcome Reception
Reception - Virtual
• 3:00 - 4:00 pm EST
Sage/Oscar Installation Help
Tutorial - Virtual
##### Tuesday, February 16, 2021
###### VIRTUAL ONLY: Sage/Oscar Days for Combinatorial Algebraic Geometry
• 9:00 - 9:45 am EST
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:30 am EST
OSCAR - The Project
Virtual
• Michael Joswig, TU Berlin & MPI Leipzig
###### Abstract
The OSCAR project is a collaborative effort to shape a new computer algebra system, written in Julia. OSCAR is built on top of the four "cornerstone systems" ANTIC (for number theory), GAP (for group and representation theory), polymake (for polyhedral and tropical geometry) and Singular (for commutative algebra and algebraic geometry). We present three examples to showcase the current version 0.5.1. This is joint work with The OSCAR Development Team.
• 10:45 - 11:15 am EST
OSCAR - Selected Features
Virtual
• Daniel Schultz, Technische Universität Kaiserslautern
###### Abstract
Introducing OSCAR, a new computer algebra system combining GAP, Polymake, Hecke and Singular.
• 11:15 - 11:30 am EST
Coffee Break
Virtual
• 11:30 am - 12:00 pm EST
Computing the Newton polytope of a large discriminant
Virtual
• Lars Kastner, Institute of Mathematics of the Technical University
###### Abstract
The Newton polytope of the discriminant of a quaternary cubic form has 166'104 vertices. One way to obtain these vertices is to enumerate all D-equivalence classes of regular triangulations of the 3- dilated tetrahedron. The only known way to do this is to enumerate all regular triangulations of the 3-dilated tetrahedron and group them into classes in a second step. This talk will focus on the computations carried out to arrive at this result. It involved the use of polymake and mptopcom on large computing clusters in parallel which in turn brought other obstacles. This software can also be used via polymake.jl in OSCAR. Since computer experiments in algebraic geometry are becoming larger and larger, this talks aims at providing insights on how to set up these experiments such that they give reliable results, and how to avoid the pitfalls we encountered. This is joint work with Robert Loewe.
• 12:15 - 12:45 pm EST
Some hybrid symbolic-numeric methods in algebraic geometry
Virtual
• Jonathan Hauenstein, University of Notre Dame
###### Abstract
On the theoretical side, algebraic geometry combines aspects of algebra and geometry to provide many tools to prove new results. On the computational side, symbolic computations typically based on algebra and numerical computations typically based on geometry can be combined to provide many new computational tools to study a variety of problems in algebraic geometry. This talk will explore some hybrid symbolic-numeric methods and applications in computational algebraic geometry.
• 1:00 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 3:00 pm EST
Problem Session
Virtual
• 3:00 - 4:00 pm EST
Contributing to Sage Tutorial
Tutorial - Virtual
##### Wednesday, February 17, 2021
###### VIRTUAL ONLY: Sage/Oscar Days for Combinatorial Algebraic Geometry
• 9:00 - 9:45 am EST
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:45 am EST
Parallelization of Triangular Decompositions- Design and implementation with the BPAS library
Virtual
• Marc Moreno, University of Western Ontario
###### Abstract
We discuss the parallelization of algorithms for solving polynomial systems by way of triangular decomposition. The "Triangularize" algorithm proceeds through incremental intersections of polynomials to produce the different components of the solution set. Independent components imply the opportunity for concurrency. This "component-level" parallelization of triangular decompositions, our focus here, belongs to the class of dynamic irregular parallelism. Potential parallel speed-up depends only on geometrical properties of the solution set (number of components, their dimensions and degrees); these algorithms do not scale with the number of processors. To manage the irregularities of component-level parallelization we combine different concurrency patterns: map, workpile, producer-consumer, pipeline and fork/join. We report on our implementation in the freely available BPAS library. Comprehensive experimentation with thousands of polynomial systems yields examples with up to 10.8-times speed up on a 12-core machine.
• 11:00 - 11:30 am EST
Coffee Break
Virtual
• 11:30 am - 12:00 pm EST
Rational integrals and periods with Sagemath and Julia
Virtual
• Pierre Lairez, INRIA
###### Abstract
Based on symbolic integration and numerical analytic continuation, we can compute to high precision integrals of multivariate rational functions. I will show applications to volume computation and to the study of quartic surfaces. I will emphasize on some software aspects, specific to Sagemath and Julia.
• 12:15 - 12:45 pm EST
Generalized cohomology quotients of the symmetric functions
Virtual
• Darij Grinberg, Drexel University
• 1:00 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 2:40 pm EST
Lightning Talks
Virtual
• Jose Brox, Centre for Mathematics of the University of Coimbra
• Juliette Bruce, University of California, Berkeley / MSRI
• Laura Brustenga i Moncusi, University of Copenhagen
• Taylor Brysiewicz, Max Planck Institute for Mathematics in the Sciences
• Papri Dey, University of Missouri
• Sean Griffin, Brown University
• Shinyoung KIM, Institute for Basic Science Center for Geometry and Physics
• 2:40 - 2:50 pm EST
Coffee Break
Virtual
• 2:50 - 3:30 pm EST
Lightning Talks
Virtual
• Lukas Kühne, Max Planck Institute for Mathematics in the Sciences
• Jianping Pan, University of California, Davis
• Marta Panizzut, TU Berlin
• Theodoros Stylianos Papazachariou, University of Essex
• Colleen Robichaux, University of Illinois at Urbana-Champaign
• Mahrud Sayrafi, University of Minnesota
• Weihong Xu, Rutgers
• 3:30 - 4:30 pm EST
Code Demonstrations
Tutorial - Virtual
##### Thursday, February 18, 2021
###### VIRTUAL ONLY: Sage/Oscar Days for Combinatorial Algebraic Geometry
• 9:00 - 9:45 am EST
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:45 am EST
msolve - A Library for Solving Polynomial Systems
Virtual
• Christian Eder, University of Kaiserslautern
###### Abstract
We present a new open source C library msolve dedicated to solve multivariate polynomial systems exactly through computer algebra methods. The core algorithmic framework of msolve relies on Gröbner bases and linear algebra based algorithms for polynomial system solving. It relies on Gröbner basis computation w.r.t. the degree reverse lexicographical order, Gröbner conversion to a lexicographical Gröbner basis and real solving of univariate polynomials. We explain in detail how these three main steps of the solving process are implemented exploiting the computational capabilities of the framework. We compare the practical performance of the different parts of msolve with similar functionalities of leading computer algebra systems such as Magma and Maple on a wide range of polynomial systems with a particular focus on those which have finitely many complex solutions, showing that msolve can tackle systems which were out of reach by the software state-of-the-art. This is joint work with Jérémy Berthomieu, Jean-Charles Faugère and Mohab Safey El Din from the PolSys Team at the Sorbonne Université in Paris.
• 11:00 - 11:30 am EST
Parallelism in Algebraic Geometry - Examples with Singular and GPI-Space
Virtual
• Anne Frühbis-Krüger, University of Oldenburg
###### Abstract
I shall illustrate the use of the Singular - GPI-space interplay in some examples including a smoothness test, GIT-fans and desingularization.
• 11:45 am - 12:45 pm EST
Coffee Break
Virtual
• 12:45 - 1:15 pm EST
Computing Galois groups in enumerative geometry
Virtual
• Frank Sottile, Texas A&M University
• 1:30 - 2:30 pm EST
Lunch/Free Time
Virtual
• 2:30 - 3:30 pm EST
Problem Session
Virtual
• 3:30 - 4:30 pm EST
Code Demonstrations
Tutorial - Virtual
##### Friday, February 19, 2021
###### VIRTUAL ONLY: Sage/Oscar Days for Combinatorial Algebraic Geometry
• 9:00 - 9:45 am EST
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:30 am EST
Factorizations into irreducibles and polytopes
Virtual
• Tommy Hofmann, TU Kaiserslautern
###### Abstract
Dedekind domains form a family of commutative rings that plays an important role in algebraic geometry and number theory. While elements of Dedekind domains factor into irreducible elements, such a factorization is in general not unique. We present an algorithm, which for a given element of the ring of integers of a number field, determines all factorizations into irreducible elements. The algorithm makes heavy use of computations with polytopes and is implemented in Oscar. This is joint work with Claus Fieker.
• 10:45 - 11:30 am EST
Computational challenges for tropical del Pezzo surfaces
Virtual
• María Angélica Cueto, Ohio State University
###### Abstract
A smooth degree d del Pezzo surface is obtained by blowing up the projective plane at (9-d) generic points. In this talk, we will discuss how to tropicalize these surfaces for various embeddings as we vary the input points and the computational challenges that arise when doing so.
• 11:15 - 11:30 am EST
Coffee Break
Virtual
• 11:30 am - 12:00 pm EST
Presenting the multipolynomial bases package
Virtual
• Viviane Pons, Université Paris Sud
###### Abstract
In this talk, we present an external SageMath package to work on multivariate polynomials seen as an algebra over integer vectors (the exponents). This allows for manipulation of divided differences operators and the definition of many bases of multivariate polynomials such as the Schubert polynomials, Grothendieck, and Demazure Characters.
• 12:15 - 12:45 pm EST
Hasse-Witt matrices and mirror toric pencils
Virtual
• 1:00 - 2:00 pm EST
Lunch/Free Time
Virtual
• 2:00 - 3:00 pm EST
Gathertown Closing Reception
Reception - Virtual
##### Monday, February 22, 2021
###### Combinatorial Algebraic Geometry
• 11:00 am - 12:00 pm EST
Grad Student/ PostDoc Professional Development: Ethics 1
Professional Development - Virtual
##### Wednesday, February 24, 2021
###### Schubert Seminar Series
• 3:30 - 4:30 pm EST
Log-Concavity of Littlewood-Richardson Coefficients
Virtual
• Avery St. Dizier, Univeristy of Illinois at Urbana-Champaign
###### Abstract
We describe a log-concavity property of the Littlewood--Richardson numbers and explain its connection to the theory of Lorentzian polynomials.
##### Thursday, February 25, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EST
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EST
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
##### Friday, February 26, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EST
Graduate Student/ PostDoc pre-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:30 am EST
CM-regularity
Post Doc/Graduate Student Seminar - Virtual
• Matthew Larson, Stanford University
• Mahrud Sayrafi, University of Minnesota
###### Abstract
The geometry of Castelnuovo-Mumford regularity - Matt Larson, Stanford University

Castelnuovo-Mumford regularity is a tool for proving effective versions of Serre vanishing. I will explain why this is frequently necessary throughout algebraic geometry. I will also define Castelnuovo-Mumford regularity, state its basic properties, and explain its relationship to syzygies of graded module.

Computing the Multigraded Castelnuovo-Mumford Regularity - Mahrud Sayrafi, University of Minnesota

Motivated by toric geometry, Maclagan-Smith defined the multigraded Castelnuovo- Mumford regularity. While this definition reduces to the usual regularity for saturated modules in P^n, some properties of the classical regularity are not yet proven to be true in the multigraded case, while others hold true with subtle differences that illuminate the differences in geometry. In this talk I will focus on the case of a product of projective spaces and describe an algorithm for computing the multigraded regularity for saturated modules implemented in Macaulay2.
• 11:30 am - 12:00 pm EST
Graduate Student/ PostDoc post-seminar break in Gather
Coffee Break - Virtual
##### Monday, March 1, 2021
###### Combinatorial Algebraic Geometry
• 11:00 am - 12:00 pm EST
Professional Development: Ethics II
Professional Development - Virtual
##### Wednesday, March 3, 2021
###### Combinatorial Algebraic Geometry
• 3:00 - 3:30 pm EST
Gathertown Afternoon Coffee
Coffee Break - Virtual
###### Schubert Seminar Series
• 4:00 - 5:00 pm EST
Quantum integrability and Grassmannians
Virtual
• Paul Zinn-Justin, The University of Melbourne
###### Abstract
We will investigate in the simplest setting, how anR-matrix'' (the building block of quantum integrable systems'') is attached to the equivariant cohomology of Grassmannians. We will compute the R-matrix in the case of CP^1 and discuss how the result generalizes to arbitrary Grassmannians. As an application, we shall derive the AJSBilley formula (restriction of Schubert classes to fixed points).
##### Thursday, March 4, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EST
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EST
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
##### Friday, March 5, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EST
Graduate Student/ PostDoc pre-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:30 am EST
Tropical Geometry
Post Doc/Graduate Student Seminar - Virtual
• Claudia Yun, Brown University
###### Abstract
The $S_n$-equivariant rational homology of the tropical moduli spaces $\Delta_{2,n}$ Abstract: Fix non-negative integers $g$ and $n$ such that $2g-2+n>0$, the tropical moduli space $\Delta_{g,n}$ is a topological space that parametrizes isomorphism classes of $n$-marked stable tropical curves of genus $g$ with total edge length 1. These spaces are important because their reduced rational homology is identified equivariantly with the top weight cohomology of the algebraic moduli spaces $M_{g,n}$, with respect to the $S_n$-action of permuting marked points. In this talk, we focus on the genus 2 case and compute the characters of $\tilde{H}_i(\Delta_{2,n};\Q)$ as $S_n$-representations for $n$ up to 8. To carry out the computations, we use a cellular chain complex for symmetric $\Delta$-complexes, a technique developed by Chan, Glatius, and Payne. The computation is done in SageMath.
• 11:30 am - 12:00 pm EST
Graduate Student/ PostDoc post-seminar break in Gather
Coffee Break - Virtual
##### Wednesday, March 10, 2021
###### Combinatorial Algebraic Geometry
• 3:00 - 3:30 pm EST
Gathertown Afternoon Coffee
Coffee Break - Virtual
###### Schubert Seminar Series
• 3:30 - 4:30 pm EST
Springer fibers and the Delta Conjecture
Virtual
• Sean Griffin, Brown University
###### Abstract
Springer fibers are a family of varieties that have remarkable connections to representation theory and combinatorics. Springer constructed an action of the symmetric group on the cohomology ring of a Springer fiber, and used it to geometrically construct the Specht modules (in type A), which are the irreducible representations of the symmetric group. In this talk, I will survey some of the many nice properties of Springer fibers. I will then introduce a new family of varieties generalizing the Springer fibers, and show how they are connected to the (recently proved) Delta Conjecture from algebraic combinatorics. We’ll then use these varieties to geometrically construct the induced Specht modules. This is joint work with Jake Levinson and Alexander Woo.
##### Thursday, March 11, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EST
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EST
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
##### Friday, March 12, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EST
Graduate Student/ PostDoc pre-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:30 am EST
Matroids
Post Doc/Graduate Student Seminar - Virtual
• Ahmed Umer Ashraf, University of Western Ontario
• Alex McDonough, Brown University
###### Abstract
Arithmetic Matroids Alex McDonough Alex will introduce matroids and show the relationship between orientable arithmetic matroids and the row lattice of integer matrices. Ahmed will give an understanding of some coefficients of the Tutte polynomial of a matroid as tropical intersection numbers. Tropical Intersection Numbers Ahmed Umer Ashraf
• 11:30 am - 12:00 pm EST
Graduate Student/ PostDoc post-seminar break in Gather
Coffee Break - Virtual
##### Monday, March 15, 2021
###### Combinatorial Algebraic Geometry
• 11:00 am - 12:00 pm EDT
Professional Development: Job Applications
Professional Development - Virtual
##### Wednesday, March 17, 2021
###### Combinatorial Algebraic Geometry
• 3:00 - 3:30 pm EDT
Gathertown Afternoon Coffee
Coffee Break - Virtual
###### Schubert Seminar Series
• 3:30 - 4:30 pm EDT
Schubert Products for Permutations with Separated Descents
Virtual
• Daoji Huang, Brown University
###### Abstract
We say that two permutations w and v have separated descents at position k if w has no descents before k and v has no descents after k. We give a counting formula in terms of reduced word tableaux for computing the structure constants of products of Schubert polynomials indexed by permutations with separated descents. This generalizes previous results by Kogan '00, rediscovered using different methods by Knutson-Yong '04, Lenart '10, and Assaf '17, that solved special cases of this separated descent problem where one of the permutations is required to have a single descent. Our approach uses generalizations of Schutzenberger's jeu de taquin and the Edelman-Greene correspondence via bumpless pipe dreams.
##### Thursday, March 18, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EDT
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EDT
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
##### Friday, March 19, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EDT
Graduate Student/postdoc pre-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:30 am EDT
Matroids and Algebra
Post Doc/Graduate Student Seminar - Virtual
• Lukas Kühne, Max Planck Institute for Mathematics in the Sciences
###### Abstract
A matroid is a combinatorial object based on an abstraction of linear independence in vector spaces and forests in graphs. I will discuss how matroid theory interacts with algebra via the so-called von Staudt constructions. These are combinatorial gadgets to encode polynomials in matroids. A main application is concerned with generalized matroid representations over division rings and matrix rings and their relation to group theory.
• 11:30 am - 12:00 pm EDT
Graduate Student/postdoc post-seminar break in Gather
Coffee Break - Virtual
##### Monday, March 22, 2021
###### VIRTUAL ONLY: Geometry and Combinatorics from Root Systems
• 10:00 - 10:15 am EDT
Welcome
Virtual
• Brendan Hassett, ICERM/Brown University
• 10:15 - 10:45 am EDT
Hey Series, Tell Me About the Extended Delta Conjecture
Virtual
• Speaker
• Jennifer Morse, University of Virginia
• Session Chair
• Leonardo Mihalcea, Virginia Polytechnic Institute and State University
###### Abstract
The space of diagonal harmonics $DH_n$ is an $S_n$-module in two sets of $n$ variables, which arose from a representation theoretic program to study Macdonald polynomials initiated by Garsia and Haiman. The doubly graded character of $DH_n$ has both a symmetric function and a combinatorial description: Haiman proved it is $\Delta'_{e_{n-1}}e_n$ for an eigenoperator $\Delta'$ of modified Macdonald polynomials, while Carlsson and Mellit established the combinatorial Shuffle Conjecture"" of Haiman, Haglund, Loehr, Remmel, and Ulyanov, expressing it as as a sum of LLT polynomials over Dyck paths. An expanded investigation led Haglund, Remmel and Wilson to the Extended Delta Conjecture, a combinatorial prediction for $\Delta_{h_l}\Delta'_{e_k}e_n$, allowing for any $0\leq l,k<n$. Bringing in new results about the action of the elliptic Hall algebra on symmetric functions, we reformulate the conjecture as the polynomial truncation of an identity of infinite series of $GL_l$ characters, expressed in terms of LLT series. The stronger infinite series identity is not difficult to prove using identities on non-symmetric Hall-Littlewood polynomials. This is joint work with Blasiak, Haiman, Pun, and Seelinger.
• 11:00 - 11:15 am EDT
Break
Coffee Break - Virtual
• 11:15 - 11:45 am EDT
Castelnuovo-Mumford regularity of matrix Schubert varieties
Virtual
• Speaker
• Oliver Pechenik, University of Waterloo
• Session Chair
• Leonardo Mihalcea, Virginia Polytechnic Institute and State University
###### Abstract
Jenna Rajchgot observed that the Castelnuovo-Mumford regularity of matrix Schubert varieties is computed by the degrees of the corresponding Grothendieck polynomials. We give a formula for these degrees. Indeed, we compute the leading terms of the top degree pieces of Grothendieck polynomials and give a complete description of when two Grothendieck polynomials have the same top degree piece (up to scalars). Our formulas rely on some new facts about major index of permutations.
• 11:45 am - 2:00 pm EDT
Lunch/Free Time
Virtual
• 2:00 - 2:30 pm EDT
Conformal blocks: an overview
Virtual
• Speaker
• Chiara Damiolini, Rutgers University
• Session Chair
• June Huh, Stanford University
###### Abstract
In this talk I will introduce simple examples of sheaves of conformal blocks arising from representations of Lie algebras and discuss how they can be used to study certain moduli spaces. I will further discuss generalizations of these sheaves which go beyond the representation theory of Lie algebras, and related works in progress.
• 2:45 - 3:15 pm EDT
Quantum geometric Satake at a root of unity and Schubert calculus for G(m,m,n)
Virtual
• Speaker
• Ben Elias, University of Oregon
• Session Chair
• June Huh, Stanford University
###### Abstract
There is a q-deformation of the reflection representation of the affine Weyl group in type A which leads to a q-deformation of many common constructions: Demazure operators, Soergel bimodules, geometric Satake, etcetera. When q is set to a root of unity, the action of the affine Weyl group factors through a finite quotient, the complex reflection group G(m,m,n), and a new kind of "Schubert calculus" appears. This talk will demonstrate this unusual construction in the well-understood case of affine A_1 and the mysterious case of affine A_2.
• 3:15 - 4:30 pm EDT
Gathertown Reception
Reception - Virtual
##### Tuesday, March 23, 2021
###### VIRTUAL ONLY: Geometry and Combinatorics from Root Systems
• 9:00 - 9:45 am EDT
Gathertown Morning Coffee
Coffee Break - Virtual
• 9:45 - 10:15 am EDT
Geometry of semi-infinite flag manifolds
Virtual
• Speaker
• Syu Kato, Kyoto University
• Session Chair
• Thomas Lam, University of Michigan
###### Abstract
Semi-infinite flag manifolds are variants of affine flag manifolds whose Schubert cells are simultaneously infinite-dimensional and infinite-codimensional. Such objects are introduced by Drinfeld and Lusztig around 1980 (as sets), and its finite-dimensional approximation model was presented by Finkelberg-Mirkovic in 1999. Recently, we described them as an explicit ind-scheme of ind-infinite type that satisfies a certain universal property. It lead us to a description of quantum $K$-groups of partial flag manifolds and some functorial relations between them. In this talk, I will start from a brief review of affine flag manifolds/varieties, define semi-infinite flag manifolds and their natural subschemes, and then explain their combinatorial and algebro-geometric properties (trying to stress the difference from affine flag manifolds/varieties). If time allows, then I will explain how some of these properties are derived as a shadow of the homological properties of affine Lie algebras. This talks is mainly based on arXiv:1810.07106.
• 10:30 - 10:45 am EDT
Break
Coffee Break - Virtual
• 10:45 - 11:35 am EDT
Lightning Talks
Virtual
• Speakers
• Aram Bingham, Tulane University
• Papri Dey, University of Missouri
• Yifeng Huang, University of Michigan
• Michael Perlman, Queen's University
• Semin Yoo, University of Rochester
• Session Chair
• David Anderson, Ohio State University
###### Abstract
Combinatorics of quadratic spaces over finite fields
Semin Yoo, University of Rochester
Let $\mathbb{F}_q^n$ be the finite field with $q$ elements, where the char$F$ is not $2$. The size of the set of $k$-dimensional subspaces of $\mathbb{F}_q^n$ is called $q$-binomial coefficient, (or Gaussian binomial coefficient.) which has various interesting combinatorial descriptions and related works. Furthermore, the fact that makes $q$-binomial coefficients more interesting is that $q$-binomial coefficients have $q$-analogues. $\mathbf{q}$-\textbf{analogues} of quantities in mathematics involve perturbations of classical quantities using the parameter $q$ and revert to the original quantities when $q$ goes to $1$. In this talk, we add one more structure, called a quadratic form. We are mainly interested in the size of the set of $k$-dimensional subspaces that have orthonormal bases, which can be also written as analogues of binomial coefficients. Various combinatorial properties of this new binomial coefficient will be discussed. We will also show what will happen in the set side if we take the limit when $q$ goes to $1$.

Mixed Hodge structure on local cohomology with support in determinantal varieties
Michael Perlman, Queen's University
Given a closed subvariety Z in a smooth variety, the local cohomology sheaves with support in Z are functorially endowed with structures as mixed Hodge modules. This implies that they are equipped with two increasing filtrations: the Hodge filtration and the weight filtration. We will discuss new calculations of these filtrations in the case when Z is a generic determinantal variety. This talk includes joint work with Claudiu Raicu.

Geometric and Combinatorial aspects of Nonlinear Algebra
Papri Dey, University of Missouri-Columbia
Nonlinear algebra is an interdisciplinary area and I shall talk about some interaction among algebraic, geometric and combinatorial objects in this field.

Clans, sects, and symmetric space closure orders
Aram Bingham, Tulane University of Louisiana
We will give a combinatorial description of the closure order on Borel orbits in symmetric spaces of Hermitian type in terms of parameterizing objects called clans and their projections onto $G/P$ (sects). This description resolves part of a conjecture of Wyser on the restriction of Bruhat orders on these spaces.

A generating function for counting mutually annihilating matrices over a finite field
Yifeng Huang, University of Michigan
We count the number of pairs of n x n matrices (A, B) over a finite field such that AB=BA=0. We then give an explicit factorization of a generating function associated to this count, which in particular shows that the function can be meromorphically extended to the entire complex plane. This essentially says that the motivic formula about (the stack of) finite-length coherent sheaves on a nodal singular curve behaves as the geometry predicts.
• 11:35 am - 2:00 pm EDT
Gathertown with Lightning speakers / Lunch
Lunch/Free Time - Virtual
• 2:00 - 2:30 pm EDT
Gröbner Geometry of Schubert Polynomials Through Ice
Virtual
• Speaker
• Anna Weigandt, University of Michigan
• Session Chair
• Angela Gibney, Rutgers University, New Brunswick
###### Abstract
The geometric naturality of Schubert polynomials and the related combinatorics of pipe dreams was established by Knutson and Miller (2005) via antidiagonal Gröbner degeneration of matrix Schubert varieties. We consider instead diagonal Gröbner degenerations. In this dual setting, Knutson, Miller, and Yong (2009) obtained alternative combinatorics for the class of vexillary matrix Schubert varieties. We will discuss general diagonal degenerations, relating them to an older formula of Lascoux (2002) in terms of the 6-vertex ice model. Lascoux's formula was recently rediscovered by Lam, Lee, and Shimozono (2018), as "bumpless pipe dreams." We will explain this connection and discuss conjectures and progress towards understanding diagonal Gröbner degenerations of matrix Schubert varieties.
• 2:45 - 3:00 pm EDT
Break
Coffee Break - Virtual
• 3:00 - 3:30 pm EDT
Rigid local systems and the multiplicative eigenvalue problem
Virtual
• Speaker
• Prakash Belkale, University of North Carolina at Chapel Hill
• Session Chair
• Angela Gibney, Rutgers University, New Brunswick
###### Abstract
Local systems are sheaves which describe the behavior of solutions of differential equations. A local system is rigid if local monodromy determines global monodromy. We give a construction which produces irreducible complex rigid local systems on a punctured Riemann sphere via quantum Schubert calculus and strange duality. These local systems are unitary and arise from a study of vertices in the polytopes controlling the multiplicative eigenvalue problem for the special unitary groups SU(n) (i.e., determination of the possible eigenvalues of a product of unitary matrices given the eigenvalues of the matrices). Roughly speaking, we show that the strange duals of the simplest vertices (which can be inductively determined) of these polytopes give (all) possible unitary irreducible rigid local systems. We note that these polytopes are generalizations of the classical Littlewood-Richardson cones of algebraic combinatorics. Answering a question of Nick Katz, we show that there are no irreducible rigid local systems on a punctured Riemann sphere of rank greater than one, with finite global monodromy, all of whose local monodromies have orders dividing n, when n is a prime number.
• 3:45 - 4:15 pm EDT
Cyclotomic generating functions
Virtual
• Speaker
• Joshua Swanson, University of California, San Diego
• Session Chair
• Angela Gibney, Rutgers University, New Brunswick
###### Abstract
Generating functions are a major theme in mathematics which unify many disciplines. It is remarkably common to find a combinatorial generating function which factors as a ratio of products of $q$-integers. Examples of such quotients arise from enumerative combinatorics (e.g. subset sums and $q$-binomials), representation theory (the $q$-Weyl dimension formula), geometry (iterated $\mathbb{P}^1$-bundles), probability (random variable decompositions), commutative algebra (homogeneous systems of parameters), and more. We call such quotients "cyclotomic generating functions" (CGFs) and initiate their general study. This talk will review some of the many known constructions of CGFs and give asymptotic estimates of their coefficients. We will also highlight a range of conjectures and accessible open problems. Joint work in progress with Sara Billey.
##### Wednesday, March 24, 2021
###### VIRTUAL ONLY: Geometry and Combinatorics from Root Systems
• 9:00 - 9:45 am EDT
Gathertown Morning Coffee
Coffee Break - Virtual
• 9:45 - 10:15 am EDT
Doing Schubert Calculus with Bumpless Pipe Dreams
Virtual
• Speaker
• Daoji Huang, Brown University
• Session Chair
• Laura Escobar, Washington University- St. Louis
###### Abstract
Bumpless pipe dreams were introduced by Lam, Lee, and Shimozono in the context of back stable Schubert calculus. Like ordinary pipe dreams, they compute Schubert and double Schubert polynomials. In this talk, I will give a bijective proof of Monk's rule for Schubert polynomials, and show that the proof extends easily to the proof of Monk's rule for double Schubert polynomials. As an application, I will explain how to biject bumpless pipe dreams and ordinary pipe dreams using the transition and co-transition formulas, which are specializations of Monk's rule. If time permits I will also briefly discuss some work on how bumpless pipe dreams can be used to compute products of certain Schubert polynomials that generalize the Grassmannian case.
• 10:30 - 10:45 am EDT
Break
Coffee Break - Virtual
• 10:45 - 11:35 am EDT
Lightning Talks
Virtual
• Speakers
• anastasia chavez, University of California, Davis
• Theo Douvropoulos, University of Massachusetts, Amherst
• Brian Hwang, Cornell University
• Maiko Serizawa, University of Ottawa
• Weihong Xu, Rutgers
• Session Chair
• Leonardo Mihalcea, Virginia Polytechnic Institute and State University
###### Abstract
Volumes of Root Zonotopes via the W-Laplacian
Theo Douvropoulos, University of Massachusetts, Amherst
The normalized volume of the classical permutahedron is given by the formula n^{n-2} which, ask any combinatorialist and they will tell you, agrees with the number of trees on n vertices. This coincidence is well understood; the classical permutahedron is a unimodular zonotope, on the set of positive roots of the Symmetric group S_n, and its bases are indexed by trees and hence enumerated by the determinant of a Laplacian matrix. This description of the permutahedron lends itself to a natural generalization: for a Weyl group W, the zonotope associated to the collection of positive roots of W will be called the root zonotope Z_W. These zonotopes Z_W are not unimodular, but their bases can be differentiated with respect to the reflection subgroup they generate (and its connection index). In joint work with Guillaume Chapuy (arxiv.2012.04519) we have introduced for any Weyl group W a (nxn) Laplacian matrix L_W whose spectrum encodes (nontrivially) many enumerative properties of W. In particular we will present new short formulas (ibid: Section 8.3) for the volumes of the root zonotopes Z_W involving only the Coxeter numbers of W and its reflection subgroups. Our approach is uniform and does not rely on the classification.

Effective point-counting for polygons in flag varieties
Brian Hwang, Cornell University
There are a number of seemingly similar "big" (e.g. affine, open) spaces that arise in the context of flag varieties. Certain classes of these spaces are known to exhibit special features. For example, open Richardson varieties have a decomposition into a disjoint union of simple components and the coordinate rings of double Bruhat cells are known to be cluster algebras. There are often combinatorial objects that govern their geometry, such as subword complexes for brick manifolds or various kinds of polytopes, especially in the context of toric varieties and related deformations and degenerations. The bestiary is rich and multifarious. Many of these spaces, however, turn out to admit a description as a polygon in a flag variety, that is, a (cyclic) tuple of flags where each flag is a prescribed distance from its immediate neighbors. Here, the distance is taken not with respect to the Euclidean metric, but with a non-symmetric Weyl-group-valued notion of "distance." Such polygons in flag varieties turn out to admit simple decompositions that can be phrased in terms of triangulations of the polygon into certain triangles with an "easy-exit" property. As an illustration of this organizing principle, we show how we can use this to easily count the points of open Richardson varieties over finite fields–––recovering a classic result of Deodhar, as well as its later enhancement by Marsh and Rietsch–––and how this naturally extends to spaces like double Bruhat cells and their amalgamations.

A 'Quantum Equals Classical' Theorem for n-pointed (K-theoretic) Gromov-Witten Invariants of Lines in Homogeneous Spaces
Weihong Xu, Rutgers University
'Quantum equals classical' refers to ways of identifying (K-theoretic) Gromov-Witten invariants on a flag variety G/P with (K-theoretic) classical invariants on a possibly different flag variety G/Q. It has been an active research topic in the last 20 years, but by far all the work has been for 3-pointed invariants. We obtain a 'quantum equals classical' theorem for n-pointed, genus 0 (T-equivariant K-theoretic) Gromov-Witten invariants of lines in G/P, which generalizes the 3-pointed result of Leonardo Mihalcea and Changzheng Li from 2013. This talk is based on joint work with Anders Buch, Linda Chen, Angela Gibney, Lauren Heller, Elana Kalashnikov, and Hannah Larson.

Matroids, Positroids, and Combinatorial Characterizations
Anastasia Chavez, UC Davis
Positroids are a special class of representable matroids introduced by Postnikov in the study of the nonnegative part of the Grassmannian. Postnikov defined several combinatorial objects that index positroids. In this talk, I'll briefly introduce some of these objects and how they can combinatorially characterize matroid properties.

Twisted quadratic foldings of root systems and combinatorial Schubert calculus
Maiko Serizawa, University of Ottawa
This thesis builds on the connection of two widely studied objects in the literature, that is, foldings of finite root systems and the structure algebras of moment graphs associated with finite root systems. Given a finite crystallographic root system <I> whose Dynkin diagram has a non­trivial automorphism, it yields a new root system <l>7 by a so-called classical folding. On the other hand, Lusztig's folding (1983) folds the root system of type Es to type H4 starting from an automorphism of the root lattice of type Es. Lanini-Zainoulline (2018) developed the notion of a twisted quadratic folding of a root system, which describes both the classical foldings and Lusztig's folding on the same footing. Our second key object of study is the structure algebra Z(Q) of the moment graph g associated with a finite root system and its reflection group W. The structure algebra Z(Q) is an algebra over a certain polynomial ring S whose underlying module is free with a distinguished basis { a( w) I w E W} called combinatorial Schubert classes. Each Schubert class a(w) is an S-valued function on W, whose value is explicitly known for any finite reflection group W. Lanini-Zainoulline (2018) showed that a twisted quadratic folding <I> -v--; <l>7 in­duces an embedding of the respective Coxeter groups E : W7 Y W and a ring homomorphism c:* : Z(Q) ➔ Z(Q7 ) between the corresponding structure algebras. This thesis investigates how the induced map c:* relates the Schubert classes of the original structure algebra Z(Q) to those of the folded structure algebra Z(Q7 ). In particular, we will provide a combinatorial criterion for a Schubert class a?u) of Z(Q7 ) to admit a Schubert class a(w) of Z(Q) such that the relation c:*(a(w) ) = c · a?u) holds for some nonzero scalar c. We will also prove that c:* is surjective after an appropriate extension of the coefficient ring.
• 11:35 am - 2:00 pm EDT
Gathertown with Lightning speakers / Lunch
Lunch/Free Time - Virtual
• 2:00 - 2:30 pm EDT
Differential operators for Schur and Schubert polynomials
Virtual
• Speaker
• Gleb Nenashev, Brown University
• Session Chair
• Alexander Yong, University of Illinois at Urbana-Champaign
###### Abstract
We study differential operators for Schur and back stable Schubert polynomials. Our operators are based on two operators of degree (-1), which satisfy Leibniz rule. For the case of Schur functions, these two operators fully determine the product of Schur functions, i.e., it is possible to define Littlewood-Richardson coefficients only using these operators. This new point of view on Schur functions gives us an elementary proof of The Giambelli identity and Jacobi-Trudi identities. For the case of Schubert polynomials, we construct a larger class of decreasing operators, which are indexed by Young diagrams. Operators from this family are related to Stanley symmetric functions. In particular, we extend bosonic operators from Schur to Schubert polynomials.
• 2:45 - 3:00 pm EDT
Break
Coffee Break - Virtual
• 3:00 - 3:30 pm EDT
Backstable K-theory Schubert calculus
Virtual
• Speaker
• Mark Shimozono, Virginia Tech
• Session Chair
• Alexander Yong, University of Illinois at Urbana-Champaign
###### Abstract
We explain some properties of back-stable limits of double Grothendieck polynomials. We discuss the dual basis of equivariant K-homology of the infinite Grassmannian.
• 3:45 - 4:15 pm EDT
Bow varieties
Virtual
• Speaker
• Richard Rimanyi, University of North Carolina at Chapel Hill
• Session Chair
• Alexander Yong, University of Illinois at Urbana-Champaign
###### Abstract
There are pairs of seemingly unrelated spaces such that Schubert calculus on the two spaces match’ in some concrete sense. This duality, called 3d mirror symmetry, is best observed in equivariant elliptic cohomology. For example, the dual of the 12-dimensional $T^*Gr(2,5)$ is a certain 4-dimensional Nakajima quiver variety. However, the set of cotangent bundles of homogeneous spaces, or even the set of quiver varieties are not closed for 3d mirror symmetry. In this talk, based on a joint work with Y. Shou, we present a larger pool of spaces: Cherkis bow varieties. Superstring theory predicts that bow varieties are closed for 3d mirror symmetry. The combinatorics necessary to play Schubert calculus on bow varieties includes binary contingency tables and tie diagrams. The existence of an operation (called Hanany-Witten transition) gives bow varieties extra flexibility. We will illustrate the combinatorics and geometry of bow varieties with examples, and we will calculate cohomological and elliptic Schubert classes (rather, stable envelopes’) to explain the matching Schubert calculus’ phenomenon.
##### Thursday, March 25, 2021
###### VIRTUAL ONLY: Geometry and Combinatorics from Root Systems
• 9:00 - 9:45 am EDT
Gathertown Morning Coffee
Coffee Break - Virtual
• 9:45 - 10:15 am EDT
Refined Dubrovin's conjecture for coadjoint varieties
Virtual
• Speaker
• Nicolas Perrin, Versailles Saint-Quentin-en-Yvelines University
• Session Chair
• Anders Buch, Rutgers University
###### Abstract
Let X be a Fano variety. Dubrovin’s conjecture predicts, among other things, an equivalence between the semi-simplicity of QH(X) the big quantum cohomology of X and the existence of a full exceptional collection in D(X) the bounded derived category of X. Recently, Kuznetsov and Smirnov proposed a refinement of this conjecture if qH(X) the small quantum cohomology is not semi-simple. I will present this conjecture, discuss it in the case of coadjoint varieties and make connections with roots systems and simple surface singularities. This is a joint work with Maxim Smirnov
• 10:30 - 10:45 am EDT
Break
Coffee Break - Virtual
• 10:45 - 11:15 am EDT
motivic Chern classes of Schubert cells and applications
Virtual
• Speaker
• Changjian Su, University of Toronto
• Session Chair
• Anders Buch, Rutgers University
###### Abstract
The motivic Chern class in K-theory is a generalization of the Chern-Schwartz-MacPherson class in homology. As the affine Hecke algebra, the motivic Chern classes of Schubert cells have a Langlands dual description. In joint works with P. Aluffi, L. Mihalcea, and J. Schurmann, we use this description to solve some problems about the Casselman basis for the p-adic dual group, and relate the Euler characteristic of the motivic Chern classes to the Iwahori-Whittaker functions.
• 11:30 am - 1:30 pm EDT
Lunch/Free Time
Virtual
• 2:00 - 2:30 pm EDT
Skew-symmetric matrix Schubert varieties
Virtual
• Speaker
• Brendan Pawlowski, University of Southern California
• Session Chair
• Thomas Lam, University of Michigan
###### Abstract
Imposing conditions on the ranks of upper-left corners of a skew-symmetric matrix defines a skew-symmetric matrix Schubert variety. We give Gröbner bases for the prime ideals of these varieties, and identify the corresponding initial ideals as the Stanley-Reisner ideals of certain explicit shellable simplicial complexes. These results are analogous to results of Knutson and Miller in the setting of ordinary matrix Schubert varieties, but the techniques are new, and can be used to give new proofs of some of their results. Based on joint work with Eric Marberg.
• 2:45 - 3:00 pm EDT
Break
Coffee Break - Virtual
• 3:00 - 3:30 pm EDT
Canonical Bases for Coulomb Branches
Virtual
• Speaker
• Harold Williams, University of Southern California
• Session Chair
• Thomas Lam, University of Michigan
###### Abstract
Coulomb branches of 4d N=2 gauge theories are a class of algebraic varieties which, together with their quantizations, appear in a variety of guises in geometry and representation theory. In this talk we outline a construction of canonical bases in the quantized coordinate rings of these varieties. These bases appear as byproducts of a more fundamental construction, a nonstandard t-structure on the dg category of coherent sheaves on the Braverman-Finkelberg-Nakajima space of triples. The heart of this t-structure is a tensor category which is not braided, but admits renormalized r-matrices abstracting those appearing in the finite dimensional representation theory of quantum affine algebras and KLR algebras. It is intended to provide a mathematical model of the category of half-BPS line defects in the relevant gauge theory, and is inspired by earlier work of Kapustin-Saulina and Gaiotto-Moore-Neitzke. On a combinatorial level, the resulting bases are expected to be controlled by specific cluster algebras, which we can confirm in simple examples. This is joint work with Sabin Cautis.
• 3:45 - 4:00 pm EDT
Break
Coffee Break - Virtual
• 4:00 - 4:30 pm EDT
Schubert puzzles from Lagrangian correspondences
Virtual
• Speaker
• Allen Knutson, Cornell University
• Session Chair
• Thomas Lam, University of Michigan
###### Abstract
Correspondences Z inside M x N induce maps on cohomology H^*(M) -> H^*(N), modulo smoothness and compactness issues. We soup up the diagonal inclusion Gr(k,n) -> Gr(k,n)^2 (whose induced cohomology map is multiplication) to a correspondence of cotangent bundles, which we then factor through T^*(a 2-step flag manifold). Grassmannian Schubert puzzles turn out to be a calculation on this intermediate manifold. As an application of this viewpoint we get a puzzle rule for the Euler characteristic of the intersection of three generically translated Bruhat cells (in up-to-4-step flag manifolds).
##### Friday, March 26, 2021
###### VIRTUAL ONLY: Geometry and Combinatorics from Root Systems
• 9:00 - 9:45 am EDT
Gathertown Morning Coffee
Coffee Break - Virtual
• 9:45 - 10:15 am EDT
A combinatorial Chevalley formula for semi-infinite flag manifolds and its applications
Virtual
• Speaker
• Cristian Lenart, University at Albany
• Session Chair
• David Anderson, Ohio State University
###### Abstract
I present a combinatorial Chevalley formula for an arbitrary weight, in the torus-equivariant K-group of semi-infinite flag manifolds, which is expressed in terms of the so-called quantum alcove model. One application is the Chevalley formula for anti-dominant fundamental weights in the (small) torus-equivariant quantum K-theory of the flag manifold G/B; this has been a longstanding conjecture. I also discuss the Chevalley formula for partial flag manifolds G/P. Another application is that the so-called quantum Grothendieck polynomials indeed represent Schubert classes in the (non-equivariant) quantum K-theory of the type A flag manifold. This is joint work with Satoshi Naito and Daisuke Sagaki.
• 10:30 - 10:45 am EDT
Break
Coffee Break - Virtual
• 10:45 - 11:15 am EDT
Coxeter-like elements, Schubert geometry, and multiplicity-freeness in algebraic combinatorics
Virtual
• Speaker
• Alexander Yong, University of Illinois at Urbana-Champaign
• Session Chair
• David Anderson, Ohio State University
###### Abstract
For a finite Coxeter system, we define “spherical elements” (extending Coxeter elements). Conjecturally, for Weyl groups, spherical elements index Levi-spherical Schubert varieties in G/B. In type A, this connects to key polynomials (Demazure characters), multiplicity-freeness, and “split-symmetry” in algebraic combinatorics. This is joint work (some ongoing) with subsets of David Brewster (UIUC), Yibo Gao (MIT), and Reuven Hodges (UIUC). See arXiv:2007.09238, arXiv:2007.09229, and arXiv:2012.09749.
• 11:30 am - 2:00 pm EDT
Lunch/Free Time
Virtual
• 2:00 - 2:30 pm EDT
Positroids, knots, and q,t-Catalan numbers
Virtual
• Speaker
• Pavel Galashin, University of California, Los Angeles
• Session Chair
• Angela Gibney, Rutgers University, New Brunswick
###### Abstract
We relate the cohomology of open positroid varieties and their point counts over finite fields to knot homology. In particular, we show that the bigraded Poincaré polynomials of top-dimensional open positroid varieties are given by rational q,t-Catalan numbers. As a consequence of the curious Lefschetz property, we obtain q,t-symmetry and unimodality statements for rational q,t-Catalan numbers. Joint work with Thomas Lam. No special background on the above objects will be assumed.
• 2:45 - 3:00 pm EDT
Break
Coffee Break - Virtual
• 3:00 - 3:30 pm EDT
Puzzle rules in cotangent Schubert calculus
Virtual
• Speaker
• Paul Zinn-Justin, The University of Melbourne
• Session Chair
• Angela Gibney, Rutgers University, New Brunswick
###### Abstract
We'll present several combinatorial rules (in terms of puzzles'') for the expansion of the product of motivic Segre classes (in equivariant K-theory) and Segre-Schwartz-MacPherson classes (in equivariant cohomology) in partial flag varieties. We'll show how to compute such classes and puzzles using the software Macaulay2.
##### Monday, March 29, 2021
###### Combinatorial Algebraic Geometry
• 11:00 am - 12:00 pm EDT
Professional Development: Hiring Process
Professional Development - Virtual
##### Wednesday, March 31, 2021
###### Combinatorial Algebraic Geometry
• 3:00 - 3:30 pm EDT
Gathertown Afternoon Coffee
Coffee Break - Virtual
###### Schubert Seminar Series
• 3:30 - 4:30 pm EDT
The isomorphism problem for Schubert varieties.
Virtual
• Edward Richmond, Oklahoma State University
###### Abstract
Schubert varieties in the full flag variety of Kac-Moody type are indexed by elements of the corresponding Weyl group. In this talk, I will discuss recent work with William Slofstra where we give a practical criterion for when two such Schubert varieties (from potentially different flag varieties) are isomorphic, in terms of the Cartan matrix and reduced words for the indexing Weyl group elements. As a corollary, we show that two such Schubert varieties are isomorphic if and only if there is an isomorphism between their integral cohomology rings that preserves the Schubert basis. As an application, we show that the isomorphism classes of Schubert varieties in a given flag variety are controlled by graph automorphisms of the Dynkin diagram.
##### Thursday, April 1, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EDT
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EDT
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
• 3:30 - 4:40 pm EDT
A trinity in affine Schubert calculus
Virtual
• Syu Kato, Kyoto University
###### Abstract
One of the most famous results in affine Schubert calculus is Peterson's quantum = affine theorem (proved by Lam-Shimozono based on a work of Mihalcea). It states that the homology of affine Grassmanian of a simple algebraic group $G$ is equivalent to the quantum cohomology of the flag manifold of $G$ as based rings. Such an equivalence has a $K$-theoretic counterpart conjectured by Lam-Li-Mihalcea-Shimozono. In this talk, we add the semi-infinite flag manifold of $G$ into this picture. In particular, the $K$-theoretic analogue of the both sides of the Peterson theorem are related to the equivariant $K$-group of the semi-infinite flag manifold. This establishes the above conjecture of Lam-Li-Mihalcea-Shimozono. Arguably, our picture provides the first explanation as to why Peterson's isomorphism should respect the basis. In addition, it has a wide range of implications including the finiteness of the quantum multiplication for the full flag manifold. This talk is based on arXiv:1805.01718. For the semi-infinite flag manifold and its equivariant $K$-group, please refer to the slide of my talk on March 23rd.
##### Friday, April 2, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EDT
Graduate Student/Postdoc pre-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:30 am EDT
Cluster Algebras and Total Positivity
Post Doc/Graduate Student Seminar - Virtual
• Sunita Chepuri, University of Michigan
###### Abstract
We will first define cluster algebras and explain their historical motivation from total positivity. The research portion of the talk will move to the setting of k-positivity, a generalization of total positivity. We will explore how much of the cluster algebraic structure of totally positive matrices extends to k-positive matrices.
• 11:30 am - 12:00 pm EDT
Graduate Student/Postdoc post-seminar break in Gather
Coffee Break - Virtual
##### Monday, April 5, 2021
###### Combinatorial Algebraic Geometry
• 11:00 am - 12:00 pm EDT
Directorate Check-In with Grads and Postdocs
Meeting - Virtual
##### Wednesday, April 7, 2021
###### Combinatorial Algebraic Geometry
• 3:00 - 3:30 pm EDT
Gathertown Afternoon Coffee
Coffee Break - Virtual
###### Schubert Seminar Series
• 2:00 - 3:00 pm EDT
The unramified affine springer fiber and the nabla operator
Virtual
• Erik Carlsson, UC Davis
###### Abstract
I'll present a new result with A. Mellit, which gives a combinatorial formula for a diagonalizing operator for the modified Macdonald polynomials, known as the nabla operator. This formula was discovered by searching for a Schubert-type basis of a certain explicit module from Haiman's polygraph theory, which is identified with both the matrix elements of this operator, and the equivariant homology of the unramified affine Springer fiber studied by Goresky, Kottwitz, and Macpherson.
##### Thursday, April 8, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EDT
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EDT
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
##### Friday, April 9, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EDT
Graduate Student/Postdoc pre-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:30 am EDT
Schubert Calculus
Post Doc/Graduate Student Seminar - Virtual
• Gleb Nenashev, Brown University
• Jianping Pan, University of California, Davis
###### Abstract
Decreasing operators for Schur functions.
Gleb Nenashev
I will discuss decreasing operators for Young diagrams. These operators give elementary proofs of some famous properties of Schur functions, e.g. for Murnaghan-Nakayama rule, Giambelli identity, and Jacobi-Trudi identities. They also fully determine Littlewood-Richardson coefficients. I will present some of these proofs. Furthermore, the decreasing operators are well defined for Back stable Schubert polynomials, but I will not discuss it.

Crystal combinatorics with stable Grothendieck polynomials
Jianping Pan
Grothendieck polynomials are representatives of Schubert varieties in the K-theory of the flag manifold. Taking stable limit, we obtain symmetric functions called the stable Grothendieck polynomials. I will talk about a combinatorial construction of it, developed by Fomin and Kirillov, which turns out to have some nice crystal structure (directed, edge-labeled graphs from representation theory). There are also several properties associated with it, including some insertion algorithms. This talk is based on arXiv:1911.08732.
• 11:30 am - 12:00 pm EDT
Graduate Student/Postdoc post-seminar break in Gather
Coffee Break - Virtual
##### Monday, April 12, 2021
###### VIRTUAL ONLY: Algebraic Geometry and Polyhedra
• 9:45 - 10:00 am EDT
Welcome
Virtual
• Brendan Hassett, ICERM/Brown University
• 10:00 - 10:45 am EDT
The Foundation of a Matroid
Virtual
• Speaker
• Matthew Baker, Georgia Institute of Technology
• Session Chair
• Lauren Williams, Harvard University
###### Abstract
Matroid theorists are typically interested in questions concerning representability of matroids over fields. More generally, one can ask about representability over partial fields in the sense of Semple and Whittle. Pendavingh and van Zwam introduced the universal partial field of a matroid, which governs the representations of over all partial fields. Unfortunately, almost all matroids are not representable over any partial field, and in this case, the universal partial field gives no information. Oliver Lorscheid and I have introduced a generalization of the universal partial field which we call the foundation of a matroid. The foundation of is a type of algebraic object which we call a pasture; pastures include both hyperfields and partial fields. As a particular application of this point of view, I will explain the classification which Lorscheid and I have recently obtained of all possible foundations for matroids having no minor isomorphic to U(2,5) or U(3,5). Among other things, our classification provides a short conceptual proof of the 1997 theorem of Lee and Scobee which says that a matroid is both ternary and orientable if and only if it is dyadic.
• 11:00 - 11:15 am EDT
Break
Coffee Break
• 11:15 am - 12:00 pm EDT
Lagrangian geometry of matroids
Virtual
• Speaker
• Graham Denham, University of Western Ontario
• Session Chair
• Lauren Williams, Harvard University
###### Abstract
In joint work with Federico Ardila and June Huh, we introduce the conormal fan of a matroid, which is the Lagrangian analogue of the Bergman fan. We use it to give a Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of a matroid. We develop tools for tropical Hodge theory to show that the conormal fan satisfies Poincaré duality, the Hard Lefschetz property, and the Hodge--Riemann relations. Together, these imply conjectures of Brylawski and Dawson about the log-concavity of the h-vectors of the broken circuit complex and independence complex of a matroid.
• 12:00 - 1:30 pm EDT
Lunch/Free Time
• 1:30 - 2:15 pm EDT
Tautological classes of matroids
Virtual
• Speaker
• Christopher Eur, Stanford University
• Session Chair
• Sam Payne, University of Texas at Austin
###### Abstract
We introduce certain torus-equivariant classes on permutohedral varieties which we call `tautological classes of matroids'' as a new geometric framework for studying matroids. Using this framework, we unify and extend many recent developments in matroid theory arising from its interaction with algebraic geometry. We achieve this by establishing a Chow-theoretic description and a log-concavity property for a 4-variable transformation of the Tutte polynomial, and by establishing an exceptional Hirzebruch-Riemann-Roch-type formula for permutohedral varieties that translates between K-theory and Chow theory. This is joint work with Andrew Berget, Hunter Spink, and Dennis Tseng.
• 2:30 - 2:45 pm EDT
Break
Coffee Break
• 2:45 - 3:30 pm EDT
Kazhdan-Lusztig theory and singular Hodge theory for matroids
Virtual
• Speaker
• June Huh, Stanford University
• Session Chair
• Sam Payne, University of Texas at Austin
###### Abstract
There is a remarkable parallel between the theory of Coxeter groups (think of the symmetric group or the dihedral group) and matroids (think of your favorite graph or point configuration) from the perspective of combinatorial cohomology theories. I will give an overview of the similarity and report on recent my joint work with Tom Braden, Jacob Matherne, Nick Proudfoot, and Botong Wang on singular Hodge theory for combinatorial geometries: https://arxiv.org/abs/2010.06088
• 3:45 - 4:45 pm EDT
Gathertown Reception
Reception - Virtual
##### Tuesday, April 13, 2021
###### VIRTUAL ONLY: Algebraic Geometry and Polyhedra
• 9:00 - 9:45 am EDT
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:45 am EDT
Real phase structures on matroid fans
Virtual
• Speaker
• Kristin Shaw, University of Oslo
• Session Chair
• Melody Chan, Brown University
###### Abstract
In this talk, I will propose a definition of real phase structures on polyhedral complexes. I’ll explain that in the case of matroid fans, specifying a real phase structure is cryptomorphic to providing an orientation of the underlying matroid. Then I’ll define the real part of a polyhedral complex with a real phase structure. This determines a closed chain in the real part of a toric variety. In the case when the polyhedral complex is a non-singular tropical variety, the real part is a PL-manifold. Moreover, for a non-singular tropical variety with a real phase structures we can apply the same spectral sequence for tropical hypersurfaces, obtained by Renaudineau and myself, to bound the Betti numbers of the real part by the dimensions of the tropical homology groups. This is joint work in progress with Johannes Rau and Arthur Renaudineau.
• 11:00 - 11:15 am EDT
Break
Coffee Break
• 11:15 am - 12:00 pm EDT
Combinatorics and real lifts of bitangents to tropical quartic curves
Virtual
• Speaker
• María Angélica Cueto, Ohio State University
• Session Chair
• Melody Chan, Brown University
###### Abstract
Smooth algebraic plane quartics over algebraically closed fields have 28 bitangent lines. By contrast, their tropical counterparts have infinitely many bitangents. They are grouped into seven equivalence classes, one for each linear system associated to an effective tropical theta characteristic on the tropical quartic curve. In this talk, I will discuss recent work joint with Hannah Markwig (arXiv:2004.10891) on the combinatorics of these bitangent classes and its connection to the number of real bitangents to real smooth quartic curves characterized by Pluecker. We will see that they are tropically convex sets and they come in 41 symmetry classes. The classical bitangents map to specific vertices of these polyhedral complexes, and each tropical bitangent class captures four of the 28 bitangents. We will discuss the situation over the reals and show that each tropical bitangent class has either zero or four lifts to classical bitangent defined over the reals, in agreement with Pluecker's classification.
• 12:00 - 1:30 pm EDT
Lunch/Free Time
• 1:30 - 2:15 pm EDT
Tropical psi classes
Virtual
• Speaker
• Renzo Cavalieri, Colorado State University
• Session Chair
• Dhruv Ranganathan, University of Cambridge
###### Abstract
We introduce a tropical geometric framework that allows us to define $\psi$ classes for moduli spaces of tropical curves of arbitrary genus. We prove correspondence theorems between algebraic and tropical $\psi$ classes for some one-dimensional families of genus-one tropical curves.
• 2:30 - 2:45 pm EDT
Break
Coffee Break
• 2:45 - 3:30 pm EDT
When are multidegrees positive?
Virtual
• Speaker
• Federico Castillo, University of Kansas
• Session Chair
• Dhruv Ranganathan, University of Cambridge
###### Abstract
The notion of multidegree for multiprojective varieties extends that of degree for projective varieties. They can be defined in geometric terms, using intersection theory, or alternatively in algebraic terms, via multigraded hilbert polynomial. We study the problem of their positivity and establish a combinatorial description using polyhedral geometry. We will show applications for Schubert polynomials and mixed volumes. This is joint work with Y.Cid-Ruiz, B.Li, J.Montano, and N.Zhang.
##### Wednesday, April 14, 2021
###### VIRTUAL ONLY: Algebraic Geometry and Polyhedra
• 9:00 - 9:45 am EDT
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:45 am EDT
Wall-crossing phenomenon for Newton-Okounkov bodies
Virtual
• Speaker
• Laura Escobar, Washington University- St. Louis
• Session Chair
• Lara Bossinger, Mathematics Institute UNAM, Oaxaca
###### Abstract
A Newton-Okounkov body is a convex set associated to a projective variety, equipped with a valuation. These bodies generalize the theory of Newton polytopes and the correspondence between polytopes and projective toric varieties. Work of Kaveh-Manon gives an explicit link between tropical geometry and Newton-Okounkov bodies. We use this link to describe a wall-crossing phenomenon for Newton-Okounkov bodies. As an example, we describe wall-crossing formula in the case of the Grassmannian Gr(2,m). This is joint work with Megumi Harada.
• 11:00 - 11:15 am EDT
Break
Coffee Break - Virtual
• 11:15 am - 12:00 pm EDT
On combinatorics of Arthur's trace formula, convex polytopes, and toric varieties
Virtual
• Speaker
• Kiumars Kaveh, University of Pittsburgh
• Session Chair
• Lara Bossinger, Mathematics Institute UNAM, Oaxaca
###### Abstract
I start by discussing two beautiful well-known theorems about decomposing a convex polytope into an signed sum of cones, namely the classical Brianchon-Gram theorem and Lawrence-Varchenko theorem. I will then explain a generalization of the Brianchon-Gram which can be summerized as ""truncating a function on the Euclidean space with respect to a polytope"". This is an extraction of the combinatorial ingredients of Arthur's ''convergence'' and ''polynomiality'' results in his famous trace formula. Arthur's trace formula concerns the trace of left action of a reductive group $G$ on the space $L^2(G / \Gamma)$ where $\Gamma$ is a discrete (arithmetic) subgroup. The combinatorics involved is closely related to compactifications of ''locally summetric spaces'' (which btw are hyperbolic manifolds). Our ''combinatorial truncation'' can be thought of as an analogue of Arthur's truncation over a toric variety (in place of a compactification of a locally symmetric space). If there is time, I will briefly sketch geometric interpretations of our combinatorial truncation as a measure and a Lefschetz number on a toric variety respectively. This is a joint work in progress with Mahdi Asgari (Oklahoma State).
• 12:00 - 1:30 pm EDT
Lunch/Free Time
• 1:30 - 2:30 pm EDT
Poster Session
Virtual
###### Abstract
Ideal Preserving Operations on Chemical Reaction Networks
Mark Curiel, University of Hawaii at Manoa
Under the assumption of mass action kinetics, the associated dynamical system of a reaction network is polynomial. We consider the ideals generated by these polynomials, which are called steady-state ideals. Steady-state ideals appear in multiple contexts within the chemical reaction network literature, however they have yet to be systematically studied. To begin such a study, we ask and partially answer the following question: when do two reaction networks give rise to the same steady-state ideal? In particular, our main results describe three operations on the reaction graph that preserve the steady-state ideal. Furthermore, since the motivation for this work is the classification of steady-state ideals, monomials play a primary role. To this end, combinatorial conditions are given to identify monomials in a steady-state ideal, and we give a sufficient condition for a steady-state ideal to be monomial.

Construction and properties of Kanev surfaces in toric 3-folds
Julius Giesler, University of Tuebingen
In this poster Kanev surfaces, which are surfaces of general type, are considered, that arise as nondegenerate hypersurfaces in toric 3-folds. First such an hypersurface might have singularities but we show how to construct a minimal and a canonical model with toric methods. After this construction we consider nondegenerate hypersurfaces with fixed Newton polytope, thus obtaining a family of Kanev surfaces, and we both compute their number of moduli and check whether the infinitesimal Torelli theorem holds for such a family. The results constitute part of the author's doctoral thesis.

On the shifted Littlewood-Richardson coefficients and the Littlewood-Richardson coefficients
Nguyen Khanh, Institut Camille Jordan
We give a new interpretation of the shifted Littlewood-Richardson coefficients $f_{\lambda\mu}^\nu$ ($\lambda,\mu,\nu$ are strict partitions). The coefficients $g_{\lambda\mu}$ which appear in the decomposition of Schur $Q$-function $Q_\lambda$ into the sum of Schur functions $Q_\lambda = 2^{l(\lambda)}\sum\limits_{\mu}g_{\lambda\mu}s_\mu$ can be considered as a special case of $f_{\lambda\mu}^\nu$ (here $\lambda$ is a strict partition of length $l(\lambda)$). We also give another description for $g_{\lambda\mu}$ as the cardinal of a subset of a set that counts Littlewood-Richardson coefficients $c_{\mu^t\mu}^{\tilde{\lambda}}$. This new point of view allows us to establish connections between $g_{\lambda\mu}$ and $c_{\mu^t \mu}^{\tilde{\lambda}}$. More precisely, we prove that $g_{\lambda\mu}=g_{\lambda\mu^t}$, and $g_{\lambda\mu} \leq c_{\mu^t\mu}^{\tilde{\lambda}}$. We conjecture that $g_{\lambda\mu}^2 \leq c^{\tilde{\lambda}}_{\mu^t\mu}$ and formulate some conjectures on our combinatorial models which would imply this inequality if it is valid.

Computational complexity, Newton polytopes, and Schubert polynomials
Colleen Robichaux, University of Illinois at Urbana-Champaign
Schubert polynomials form a basis of all polynomials and appear in the study of cohomology rings of flag manifolds. The nonvanishing problem asks if a coefficient of a Schubert polynomial is nonzero. We give a tableau criterion for nonvanishing, from which we deduce the first polynomial time algorithm. These results are obtained from new characterizations of the Schubitope, a generalization of the permutahedron defined for any subset of the nxn grid. This is joint work with Anshul Adve and Alexander Yong.

Enumeration of algebraic and tropical singular hypersurfaces
Uriel Sinichkin, Tel Aviv University
We develop a version of Mikhalkin's lattice path algorithm for projective hypersurfaces of arbitrary degree and dimension, which enumerates singular tropical hypersurfaces passing through appropriate configuration of points. By proving a correspondence theorem combined with the lattice path algorithm, we construct a $\delta$ dimensional linear space of degree $d$ real hypersurfaces containing $\frac{1}{\delta!}(\gamma_nd^n)^{\delta}+O(d^{n\delta-1})$ hypersurfaces with $\delta$ real nodes, where $\gamma_n$ are positive and given by a recursive formula.
This is asymptotically comparable to the number $\frac{1}{\delta!} \left( (n+1)(d-1)^n \right)^{\delta}+O\left(d^{n(\delta-1)} \right)$ of complex hypersurfaces having $\delta$ nodes in a $\delta$ dimensional linear space. In the case $\delta=1$ we give a slightly better leading term.
• 2:30 - 3:15 pm EDT
On Newton-Okounkov bodies associated to Grassmannians
Virtual
• Speaker
• Alfredo Nájera Chávez, Mathematics Institute UNAM, Oaxaca
• Session Chair
• Travis Mandel, University of Oklahoma
###### Abstract
In this talk I will elaborate on a certain class of Newton-Okounkov bodies that one can associate to "nice" compactifications of cluster varieties. In particular, I will explain how this approach recovers Rietsch--Williams' construction of Newton--Okounkov bodies for Grassmannians. In order to make the precise connection it will be necessary to explain how the Marsh--Rietsch potential and the Gross--Hacking--Keel--Kontsevich potential for Grassmannians are related. Finally, I will draw some consequences from this relation such as an isomorphism of the toric degenerations obtained by Rietsch-Willimas and the toric degenerations obtained by the celebrated "principal coefficient" construction. Time permitting, I will briefly elaborate on the interpretation of these results from the viewpoint of the representation theory of the associated dimer algebra.
• 3:30 - 3:45 pm EDT
Break
Coffee Break
• 3:45 - 4:30 pm EDT
Broken line convexity
Virtual
• Speaker
• Timothy Magee, University of Birmingham
• Session Chair
• Daping Weng, Michigan State University
###### Abstract
In this talk, I'll give an overview of how convex polytopes generalizes from the toric world to the cluster world, where the "polytopes" live in a tropical space rather than a vector space. In this setting, "broken line convex polytopes" define projective compactifications of cluster varieties. After this overview, I'll focus on two exciting applications of this more general notion of convexity: 1) an intrinsic version of Newton-Okounkov bodies and 2) a possible cluster version of a classic toric mirror symmetry construction due to Batyrev. The overview is based on joint work with Mandy Cheung and Alfredo Nájera Chávez, and the applications are based on ongoing joints works with Mandy, Alfredo, Lara Bossinger, and Bosco Frías Medina.
##### Thursday, April 15, 2021
###### VIRTUAL ONLY: Algebraic Geometry and Polyhedra
• 9:00 - 9:45 am EDT
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:45 am EDT
Toric vector bundles -- an overview
Virtual
• Speaker
• Milena Hering, The University of Edinburgh
• Session Chair
• Linda Chen, Swarthmore College
###### Abstract
I will give a brief introduction to toric vector bundles, an overview of what we know about them so far, and explain some more recent developments on the defining equations of embeddings of their projectivisations
• 11:00 - 11:15 am EDT
Break
Coffee Break
• 11:15 am - 12:00 pm EDT
The Fulton-MacPherson compactification is not a Mori dream space
Virtual
• Speaker
• José González, University of California, Riverside
• Session Chair
• Linda Chen, Swarthmore College
###### Abstract
We show that the Fulton-MacPherson compactification of the configuration space of n distinct labeled points in certain varieties of arbitrary dimension d, including projective space, is not a Mori dream space for n greater than or equal to d+9.
• 12:00 - 1:30 pm EDT
Lunch/Free Time
• 1:30 - 2:15 pm EDT
Schubert polynomials from a polytopal point of view
Virtual
• Speaker
• Karola Meszaros, Cornell University
• Session Chair
• Laura Escobar, Washington University- St. Louis
###### Abstract
Schubert polynomials are multivariate polynomials representing cohomology classes on the flag manifold. Despite the beautiful formulas developed for them over the past three decades, the coefficients of these polynomials remained mysterious. I will explain Schubert polynomials from a polytopal point of view, answering, at least partially, the questions: Which coefficients are nonzero? How do the coefficients compare to each other in size? Are the Newton polytopes of these polynomials saturated? Are their coefficients log-concave along lines? Is there a polytope whose integer point transform specializes to Schubert polynomials? As the questions themselves suggest, we will find that polytopes play an outsized role in our understanding. The talk is based on joint works with Alex Fink, June Huh, Ricky Liu, Jacob Matherne and Avery St. Dizier.
• 2:30 - 2:45 pm EDT
Break
Coffee Break
• 2:45 - 3:30 pm EDT
Families of Gröbner degenerations
Virtual
• Speaker
• Lara Bossinger, Mathematics Institute UNAM, Oaxaca
• Session Chair
• Laura Escobar, Washington University- St. Louis
###### Abstract
Let V be the weighted projective variety defined by a weighted homogeneous ideal J and C a maximal cone in the Gröbner fan of J with m rays. We construct a flat family over affine m-space that assembles the Gröbner degenerations of V associated with all faces of C. This is a multi-parameter generalization of the classical one-parameter Gröbner degeneration associated to a weight. We explain how our family can be constructed from Kaveh--Manon's recent work on the classification of toric flat families over toric varieties: it is the pull-back of a toric family defined by a Rees algebra with base the toric variety associated to cone C along its universal torsor. We apply this construction to the Grassmannians of planes with their Plücker embeddings and the Grassmannian Gr(3,6) with its cluster embedding. In each case there exists a unique maximal Gröbner cone whose associated initial ideal is the Stanley--Reisner ideal of the cluster complex. We show that the corresponding cluster algebra with universal coefficients arises as the algebra defining the flat family associated to this cone. This talk is based on joint work with F. Mohammadi and A. Nájera Chávez, arxiv:2007.14972.
##### Friday, April 16, 2021
###### VIRTUAL ONLY: Algebraic Geometry and Polyhedra
• 9:00 - 9:45 am EDT
Gathertown Morning Coffee
Coffee Break - Virtual
• 10:00 - 10:45 am EDT
The logarithmic Hilbert scheme of curves
Virtual
• Speaker
• Dhruv Ranganathan, University of Cambridge
• Session Chair
• Federico Ardila, San Francisco State University
###### Abstract
Within the Hilbert scheme of curves in projective space is a subscheme of curves that are "tropical" in the sense of Tevelev: they interact well with the coordinate subspaces. I will explain why, from the point of view of tropical and logarithmic geometry, this locus ought to be the principal open cell in another moduli space, of which the Hilbert scheme is only an approximation. This "logarithmic Hilbert scheme" was recently constructed in work with Davesh Maulik (MIT) and is the core of a new theory of logarithmic Donaldson-Thomas invariants. The story touches another major character in the story of polyhedral and algebraic geometry: the secondary polytope of Gel'fand-Kapranov-Zelevinsky. I'll try to give some sense for why.
• 11:00 - 11:15 am EDT
Break
Coffee Break
• 11:15 am - 12:00 pm EDT
Initial degenerations of Grassmannians
Virtual
• Speaker
• Daniel Corey, University of Wisconsin, Madison
• Session Chair
• Federico Ardila, San Francisco State University
###### Abstract
We construct closed immersions from initial degenerations of Gr_0(d,n)---the open cell in the Grassmannian Gr(d,n) given by the nonvanishing of all Plücker coordinates---to limits of thin Schubert cells associated to diagrams induced by the face poset of the corresponding tropical linear space. These are isomorphisms in many cases, including (d,n) equal to (2,n), (3,6) and (3,7). As an application, Gr_0(3,7) is schön, and the Chow quotient of Gr(3,7) by the maximal torus in PGL(7) is the log canonical compactification of the moduli space of 7 points in P^2 in linear general position, making progress on a conjecture of Hacking, Keel, and Tevelev. Time permitting, I will discuss recent work on extending these results to the Lie-type D setting.
• 12:00 - 1:30 pm EDT
Lunch/Free Time
• 1:30 - 2:15 pm EDT
On the top-weight rational cohomology of A_g
Virtual
• Speaker
• Melody Chan, Brown University
• Session Chair
• Yoav Len, University of St Andrews
###### Abstract
I'll report on recent work using tropical techniques to find new rational cohomology classes in moduli spaces A_g of abelian varieties, building on previous joint work with Galatius and Payne on M_g. Joint work with Madeline Brandt, Juliette Bruce, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.
• 2:30 - 2:45 pm EDT
Break
Coffee Break
• 2:45 - 3:30 pm EDT
Tropical Flag Varieties
Virtual
• Speaker
• Session Chair
• Yoav Len, University of St Andrews
###### Abstract
Flag matroids are combinatorial abstractions of flags of linear subspaces, just as matroids are of linear subspaces. We introduce the flag Dressian as a tropical analogue of the partial flag variety, and give a correspondence between: (a) points on the flag Dressian, (b) valuated flag matroids, (c) flags of projective tropical linear spaces, and (d) coherent flag matroidal subdivisions of the flag matroid polytope. The ideas presented in this talk will be brought to life through examples.
##### Monday, April 19, 2021
###### Combinatorial Algebraic Geometry
• 11:00 am - 12:00 pm EDT
Papers and Journals
Professional Development - Virtual
##### Wednesday, April 21, 2021
###### Combinatorial Algebraic Geometry
• 3:00 - 3:30 pm EDT
Gathertown Afternoon Coffee
Coffee Break - Virtual
###### Schubert Seminar Series
• 3:30 - 4:30 pm EDT
Schubert Calculus via bosonic operators
Virtual
• Gleb Nenashev, Brown University
###### Abstract
I will present a definition and some important properties of the bosonic operators for back-stable Schubert polynomials. The operators act on the left weak Bruhat order (divided difference and Monk’s rule use the right side action on permutations in my notations). These operators with an extra condition give sufficiently enough linear equations for the structure constants of flag varieties. In particular, they provide a recurrent formula for the structure constants. In some special cases it is easy to check the positivity of the structure constants using this formula, examples will be presented. One of the advantages of our method is that we do not need to use formulas for Schubert polynomials and back-stable Schubert polynomials. Nevertheless if time permits, I will also show how to establish the pipe dreams formula using these operators.
##### Thursday, April 22, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EDT
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EDT
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
• 3:30 - 4:40 pm EDT
Bow Varieties---Combinatorics, Geometry, and Characteristic Classes
Virtual
• Speaker
• Yiyan Shou, UNC - Chapel Hill
• Session Chair
• Anders Buch, Rutgers University
###### Abstract
Cherkis bow varieties are believed to be a natural setting for the study of 3d (N=4) mirror symmetry from the perspective of characteristic classes. This talk will review the "quiver" definition of bow varieties, due to Nakajima and Takayama, and introduce a combinatorial framework for their study. This framework includes brane diagrams and related combinatorial operations and constructions. Using this combinatorial framework, we will analyze the tangent bundle, torus fixed points, and invariant curves, key ingredients for defining characteristic classes. Finally, examples of cohomological stable envelopes will be calculated. This talk is based on a joint work with Richárd Rimányi.
##### Friday, April 23, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EDT
Graduate Student/postdoc post-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:00 am EDT
Slack realization spaces and realizability of polytopes
Post Doc/Graduate Student Seminar - Virtual
• Antonio Macchia, Freie Universität Berlin
• 11:00 - 11:30 am EDT
Introduction to Hessenberg varieties
Post Doc/Graduate Student Seminar - Virtual
• Sean Griffin, Brown University
###### Abstract
Hessenberg varieties are a family of subvarieties of the complete flag variety that have many wonderful combinatorial properties. I'll survey some of these combinatorial properties, including an amazing connection to chromatic quasisymmetric functions, which was conjectured by Shareshian and Wachs and proven by Brosnan and Chow.
• 11:30 am - 12:00 pm EDT
Graduate Student/postdoc post-seminar break in Gather
Coffee Break - Virtual
##### Monday, April 26, 2021
###### Combinatorial Algebraic Geometry
• 11:00 am - 12:00 pm EDT
Grant Proposals
Professional Development - Virtual
##### Wednesday, April 28, 2021
###### Combinatorial Algebraic Geometry
• 3:00 - 3:30 pm EDT
Gathertown Afternoon Coffee
Coffee Break - Virtual
###### Schubert Seminar Series
• 3:30 - 4:30 pm EDT
The Abelian/non-Abelian correspondence and mirror symmetry
Virtual
• Elana Kalashnikov, Harvard University
###### Abstract
The Abelian/non-Abelian correspondence is a powerful tool that can be used to study GIT quotients V//G, where V is a vector space. Such GIT quotients include type A flag varieties and quiver flag varieties. The principle of the Abelian/non-Abelian correspondence is that a GIT quotient V//G can be studied by considering the much simpler Abelian GIT quotient V//T, where T is maximal torus of G. I'll discuss applications of the Abelian/non-Abelian correspondence to quantum cohomology and mirror symmetry of type A flag varieties and quiver flag varieties, focusing on rim-hook removal rules and Plücker coordinate mirrors. Part of this talk will report on joint work with Wei Gu.
##### Thursday, April 29, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EDT
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EDT
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
##### Friday, April 30, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EDT
Graduate Student/postdoc pre-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:30 am EDT
Toric Geometry
Post Doc/Graduate Student Seminar - Virtual
• Sean Griffin, Brown University
• Mariel Supina, University of California, Berkeley
###### Abstract
An introduction to toric geometry
Sean Griffin, Brown University
I'll introduce the basics of toric geometry, including the construction of a toric variety from a rational convex polytope. We'll do lots of examples to illustrate the ideas.

The equivariant Ehrhart theory of the permutahedron
Mariel Supina, University of California, Berkeley
Ehrhart theory is a topic in geometric combinatorics which involves counting the lattice points inside of lattice polytopes. Stapledon (2010) introduced equivariant Ehrhart theory and conjectured a relationship between the equivariant H*-series of a polytope and invariant hypersurfaces in its corresponding toric variety. In this talk, I will describe Stapledon's conjecture and discuss joint work with Ardila and Vindas Meléndez (2020) on verifying his conjecture in this special case.
• 11:30 am - 12:00 pm EDT
Graduate Student/postdoc post-seminar break in Gather
Coffee Break - Virtual
##### Wednesday, May 5, 2021
###### Combinatorial Algebraic Geometry
• 3:00 - 3:30 pm EDT
Gathertown Afternoon Coffee
Coffee Break - Virtual
###### Schubert Seminar Series
• 3:30 - 4:30 pm EDT
Equivariant Schubert Calculus of Peterson Varieties
Virtual
• Rahul Singh, Virginia Polytechnic Institute and State University
###### Abstract
Peterson varieties are certain singular subvarieties of flag manifolds, naturally admitting one-dimensional torus action. Starting with a natural basis for the equivariant homology of a Peterson variety, we construct a dual basis in cohomology and show that the structure constants of the cohomology ring are positive with respect to this basis. We also discuss the sense in which the fundamental classes of the Peterson varieties exhibit a stability analogous to the stability of Schubert classes, and how this can be used to streamline various calculations in the Schubert calculus of Peterson varieties. This is joint work with Rebecca Goldin and Leonardo Mihalcea.
##### Thursday, May 6, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 11:00 am EDT
Learning Seminar - Differential forms on tropical moduli spaces
Seminar - Virtual
• Melody Chan, Brown University
• Sam Payne, University of Texas at Austin
###### Abstract
The goal is to understand Francis Brown's recent arXiv preprint Invariant differential forms on complexes of graphs and Feynman integrals. A sub-goal, which we hope takes shape over the course of the seminar, is to draw out the connection between Brown's article and tropical moduli spaces of curves and abelian varieties.

This is not an introductory seminar per se in that the choice of topic is of specialized interest and of particular interest to us vis-a-vis our current work. On the other hand, we will try to develop the machinery without relying on background from tropical geometry, much as Brown's article is able to do.

Resources to get started:

1. Sam's lectures from the introductory Workshop, available from the webpage

2. Draft of a survey articleon classical/tropical moduli spaces by Melody, which outlines the appearance of graph complexes in the study of tropical moduli.
• 11:00 am - 12:00 pm EDT
Semistable Reduction Seminar
Seminar - Virtual
• Dan Abramovich, Brown University
• 12:00 - 1:00 pm EDT
Socially Distanced Walk with Directorate
Socially Distanced Walk - 121 South Main Street Main Entrance
##### Friday, May 7, 2021
###### Combinatorial Algebraic Geometry
• 10:00 - 10:30 am EDT
Graduate Student/postdoc pre-seminar break in Gather
Coffee Break - Virtual
• 10:30 - 11:30 am EDT
Kac-Moody Schubert calculus
Post Doc/Graduate Student Seminar - Virtual
• Shuai Jiang, Virginia Tech
###### Abstract
Equivariant homology of infinite Grassmannian
Let G be a semisimple algebraic group over C, B ⊂ G a Borel subgroup and T a maximal torus. Peterson discovered the ”quantum equals affine” phenomena and Lam and Shimozono proved that the equivariant Schubert homology structure constants of affine Grassmannian are the Schubert structure constants for the T-equivariant quantum cohomology rings QHT(G/B). Later, Lam and Shimozono found the equivariant homology Chevalley formula and more recently Lam, Lee and Shimozono use this formula to derive the j-basis coefficients of infinity Grassmannian for a hook. In the first part of this talk, I will discuss the j-basis in equivariant homology of affine Grassmannian. Then, I will explain their hook-formula.
• 11:30 am - 12:00 pm EDT
Graduate Student/postdoc post-seminar break in Gather
Coffee Break - Virtual

All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).

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