Organizing Committee
 Anders Buch
Rutgers University  Leonardo Mihalcea
Virginia Polytechnic Institute and State University
Abstract
The seminar is aimed at graduate students and early career researchers, and it will showcase both surveys of particular topics, and the latest developments, in Schubert Calculus and related areas. All speakers are encouraged to make at least the first half of their talks introductory and strictly accessible to graduate students.
Talks will be Wednesdays from 3:30 PM 4:30 PM ET. See the schedule below for details.
Workshop Schedule
Wednesday, February 24, 2021

3:30  4:30 pm EST
Wednesday, March 3, 2021

4:00  5:00 pm ESTQuantum integrability and GrassmanniansVirtual
 Paul ZinnJustin, The University of Melbourne
Abstract
We will investigate in the simplest setting, how an``Rmatrix'' (the building block of ``quantum integrable systems'') is attached to the equivariant cohomology of Grassmannians. We will compute the Rmatrix 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).
Wednesday, March 10, 2021

3:30  4:30 pm ESTSpringer fibers and the Delta ConjectureVirtual
 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.
Wednesday, March 17, 2021

3:30  4:30 pm EDTSchubert Products for Permutations with Separated DescentsVirtual
 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 KnutsonYong '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 EdelmanGreene correspondence via bumpless pipe dreams.
Wednesday, March 31, 2021

3:30  4:30 pm EDTThe isomorphism problem for Schubert varieties.Virtual
 Edward Richmond, Oklahoma State University
Abstract
Schubert varieties in the full flag variety of KacMoody 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.
Wednesday, April 7, 2021

2:00  3:00 pm EDTThe unramified affine springer fiber and the nabla operatorVirtual
 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 Schuberttype 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.
Wednesday, April 21, 2021

3:30  4:30 pm EDTSchubert Calculus via bosonic operatorsVirtual
 Gleb Nenashev, Brown University
Abstract
I will present a definition and some important properties of the bosonic operators for backstable 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 backstable Schubert polynomials. Nevertheless if time permits, I will also show how to establish the pipe dreams formula using these operators.
Wednesday, April 28, 2021

3:30  4:30 pm EDTThe Abelian/nonAbelian correspondence and mirror symmetryVirtual
 Elana Kalashnikov, Harvard University
Abstract
The Abelian/nonAbelian 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/nonAbelian 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/nonAbelian correspondence to quantum cohomology and mirror symmetry of type A flag varieties and quiver flag varieties, focusing on rimhook removal rules and Plücker coordinate mirrors. Part of this talk will report on joint work with Wei Gu.
Wednesday, May 5, 2021

3:30  4:30 pm EDTEquivariant Schubert Calculus of Peterson VarietiesVirtual
 Rahul Singh, Virginia Polytechnic Institute and State University
Abstract
Peterson varieties are certain singular subvarieties of flag manifolds, naturally admitting onedimensional 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.
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Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Dan Abramovich
Brown University

Ashleigh Adams
UC Davis

Adam Afandi
Colorado State University

Tair Akhmejanov
University of CaliforniaDavis

Kamyar Amini
Sharif University of Technology

David Anderson
Ohio State University

Federico Ardila
San Francisco State University

Ahmed Umer Ashraf
University of Western Ontario

Olga Azenhas
University of Coimbra

Christin Bibby
Louisiana State University

Sara Billey
University of Washington

Aram Bingham
Tulane University

Madeline Brandt
Brown University

Michel Brion
Université Grenoble Alpes

Juliette Bruce
University of California, Berkeley / MSRI

Anders Buch
Rutgers University

Amanda Burcroff
Durham University

Mahir Bilen Can
Tulane University

Erik Carlsson
UC Davis

Melody Chan
Brown University

Anastasia Chavez
University of California, Davis

Linda Chen
Swarthmore College

Sunita Chepuri
University of Michigan

Xinle Dai
University of Waterloo

Papri Dey
University of Missouri

Theo Douvropoulos
University of Massachusetts, Amherst

Anne Dranowski
Institute for Advanced Study

Balazs Elek
Cornell University

Laura Escobar
Washington University St. Louis

Christopher Eur
Stanford University

Matthew Faust
Texas A&M University

Netanel Friedenberg
Yale University

William Fulton
University of Michigan

Nir Gadish
MIT

Maria Gillespie
Colorado State University

Andrey Glubokov
Ave Maria University

Vassily Gorbounov
Higher School of Economics, Russia

Elisa Gorla
University of Neuchatel

Eugene Gorsky
UC Davis

Sean Griffin
Brown University

Kangjin Han
DaeguGyeongbuk Institute of Sciences and Technology (DGIST)

Megumi Harada
MCMASTER UNIVERSITY

Milena Hering
The University of Edinburgh

Yifeng Huang
University of Michigan

Daoji Huang
Brown University

Anthony Iarrobino
Northeastern University

Bogdan Ion
University of Pittsburgh

David Jensen
University of Kentucky

Shuai Jiang
Virginia Tech

Michael Joswig
TU Berlin & MPI Leipzig

Nidhi Kaihnsa
Brown University

Elana Kalashnikov
Harvard University

Siddarth Kannan
Brown University

Syu Kato
Kyoto University

Hannah Keese
Cornell University

Gary Kennedy
Ohio State University

Nguyen Khanh
Institut Camille Jordan

Patricia Klein
University of Minnesota

Allen Knutson
Cornell University

Jakub Koncki
Institute of Mathematics, Polish Academy of Sciences

Lukas Kühne
Max Planck Institute for Mathematics in the Sciences

Thomas Lam
University of Michigan

Matthew Larson
Stanford University

KangJu Lee
Seoul National University

Shiyue Li
Brown University

David LowryDuda
ICERM & Brown University

Antonio Macchia
Freie Universität Berlin

Olya Mandelshtam
University of Waterloo

Madhusudan Manjunath
INDIAN INSTITUTE OF TECHNOLOGY BOMBAY

Hannah Markwig
Eberhard Karls University of Tübingen

Mikhail Mazin
Kansas State University

Alex McDonough
Brown University

Leonardo Mihalcea
Virginia Polytechnic Institute and State University

Elizabeth Milićević
Haverford College

Fatemeh Mohammadi
University of Bristol

Philippe Nadeau
Institut Camille Jordan

Hiroshi Naruse
University of Yamanashi

Gleb Nenashev
Brown University

David Oetjen
Virginia Tech

Daniel Orr
Virginia Tech

Jianping Pan
University of California, Davis

Sam Payne
University of Texas at Austin

Nicolas Perrin
Versailles SaintQuentinenYvelines University

Nathan Pflueger
Amherst College

Zhijun (George) Qiao
University of Texas Rio Grande Valley

Rohini Ramadas
Brown University

Edward Richmond
Oklahoma State University

Konstanze Rietsch
King's College London

Richard Rimanyi
University of North Carolina at Chapel Hill

Colleen Robichaux
University of Illinois at UrbanaChampaign

Mahrud Sayrafi
University of Minnesota

Hal Schenck
Iowa State University

Maiko Serizawa
University of Ottawa

Melissa ShermanBennett
UC Berkeley/Harvard

Ryan Shifler
Salisbury University

Connor Simpson
University of Wisconsin  Madison

Rahul Singh
Virginia Polytechnic Institute and State University

MirunaStefana Sorea
SISSA, Trieste

Avery St. Dizier
Univeristy of Illinois at UrbanaChampaign

Eric Stucky
University of MinnesotaTwin Cities

Changjian Su
University of Toronto

Yuri Sulyma
Brown University

Mariel Supina
University of California, Berkeley

Anna Tao
Brown University

Nicola Tarasca
Virginia Commonwealth University

Mihail Tarigradschi
Rutgers University

Andrew Tawfeek
University of Washington

Ayush Tewari
Eberhard Karls Universitat Tubingen

Jeremy Usatine
Brown University

Ravi Vakil
Stanford University

Lorenzo Vecchi
Alma Mater Studiorum  Università di Bologna

Emanuele Ventura
University of Bern

Andrzej Weber
Uniwersity of Warsaw

Anna Weigandt
University of Michigan

Lauren Williams
Harvard University

Corey Wolfe
Tulane University

Cameron Wright
University of Washington

Weihong Xu
Rutgers

Damir Yeliussizov
KazakhBritish Technical University

Alexander Yong
University of Illinois at UrbanaChampaign

Semin Yoo
University of Rochester

Chi Ho Yuen
Brown University

Claudia Yun
Brown University

Paul ZinnJustin
The University of Melbourne