Organizing Committee
 Anders Buch
Rutgers University  Wolfram Decker
Technische Universität Kaiserslautern  Benjamin Hutz
Saint Louis University  Michael Joswig
TU Berlin & MPI Leipzig  Julian Rüth
none  Anne Schilling
UC Davis
Abstract
This workshop will focus on the development of software to facilitate research in combinatorial algebraic geometry, based on the SAGE Mathematical Software System and the OSCAR Computer Algebra System. Special attention will be given to efficient computations with multivariate polynomials, which is a critical part of many algorithms in combinatorial algebraic geometry. Aside from development of software, the workshop will feature a series of talks about polynomial computations, as well as introductory lectures about Sage and Oscar.
Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Simonetta Abenda
Università di Bologna

Guillermo Aboumrad
Stanford University

Dan Abramovich
Brown University

Ashleigh Adams
UC Davis

Adam Afandi
Colorado State University

Tair Akhmejanov
University of CaliforniaDavis

Elie Alhajjar
US Military Academy

David Anderson
Ohio State University

Federico Ardila
San Francisco State University

Ahmed Umer Ashraf
University of Western Ontario

Matthew Baker
Georgia Institute of Technology

Mara Belotti
Technische Universität

Christin Bibby
Louisiana State University

Sara Billey
University of Washington

Simone Billi
University of Bologna

Aram Bingham
Tulane University

Janko Boehm
TU Kaiserslautern

Alin Bostan
INRIA

Madeline Brandt
Brown University

Paul Breiding
Technische Universität Berlin

Michel Brion
Université Grenoble Alpes

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

Anders Buch
Rutgers University

Daniel Bump
Stanford University

Amanda Burcroff
Durham University

Mahir Bilen Can
Tulane University

Eduardo Cattani
University of Massachusetts Amherst

Ian Cavey
The Ohio State University

Seth Chaiken
University at Albany

Melody Chan
Brown University

PierreEmmanuel Chaput
université de Lorraine

Anastasia Chavez
University of California, Davis

Sunita Chepuri
University of Michigan

ManWai Cheung
Harvard University

Daniel Corey
University of Wisconsin, Madison

María Angélica Cueto
Ohio State University

Mark Curiel
University of Hawaii at Manoa

Xinle Dai
Harvard University

Wolfram Decker
Technische Universität Kaiserslautern

Hamdi Dervodeli
Kyoto University

Papri Dey
University of Missouri

Theo Douvropoulos
University of Massachusetts, Amherst

Anne Dranowski
Institute for Advanced Study

Nicholas Early
Institute for Advanced Study

Holger Eble
TU Berlin

Christian Eder
University of Kaiserslautern

Laura Escobar
Washington University St. Louis

Christopher Eur
Stanford University

Matthew Faust
Texas A&M University

Luis Ferroni
University of Bologna

Claus Fieker
University of Kaiserslautern

Sergey Fomin
University of Michigan

Netanel Friedenberg
Yale University

Anne FrühbisKrüger
University of Oldenburg

William Fulton
University of Michigan

Nir Gadish
MIT

Pavel Galashin
University of California, Los Angeles

Marina GarroteLópez
Universitat Politècnica de Catalunya

Jack Garzella
University of California, San Diego

Alheydis Geiger
Eberhard Karls University Tübingen

Andrey Glubokov
Ave Maria University

Eugene Gorsky
UC Davis

Sean Griffin
Brown University

Darij Grinberg
Drexel University

Samuel Grushevsky
Stony Brook University

Aziz Burak Guelen
The Ohio State University

Emily Gunawan
University of Oklahoma

Christian Haase
Freie Universität Berlin

Kangjin Han
DaeguGyeongbuk Institute of Sciences and Technology (DGIST)

Megumi Harada
MCMASTER UNIVERSITY

Jonathan Hauenstein
University of Notre Dame

Oskar Henriksson
University of Copenhagen

Milena Hering
The University of Edinburgh

María Herrero
University of Buenos Aires  CONICET

Tommy Hofmann
TU Kaiserslautern

Max Horn
Technische Universität Kaiserslautern

Serkan Hosten
San Francisco State University

Yifeng Huang
University of Michigan

Daoji Huang
Brown University

June Huh
Stanford University

Benjamin Hutz
Saint Louis University

Brian Hwang
Cornell University

Anthony Iarrobino
Northeastern University

Bogdan Ion
University of Pittsburgh

Alexey Izmailov
Brown University

David Jensen
University of Kentucky

Shuai Jiang
Virginia Tech

Michael Joswig
TU Berlin & MPI Leipzig

Nidhi Kaihnsa
Brown University

Marek Kaluba
Technische Universität Berlin

Siddarth Kannan
Brown University

Lars Kastner
Institute of Mathematics of the Technical University

Kiran Kedlaya
University of California, San Diego

Gary Kennedy
Ohio State University

Nguyen Khanh
Institut Camille Jordan

Shinyoung Kim
Institute for Basic Science Center for Geometry and Physics

Patricia Klein
University of Minnesota

Allen Knutson
Cornell University

Jakub Koncki
Institute of Mathematics, Polish Academy of Sciences

Matthias Köppe
UC Davis

Gaurish Korpal
University of Arizona

Lukas Kühne
Max Planck Institute for Mathematics in the Sciences

Pierre Lairez
INRIA

Thomas Lam
University of Michigan

Matthew Larson
Stanford University

Samuel Lelièvre
Université ParisSaclay

Anton Leykin
Georgia Tech

Shiyue Li
Brown University

David LowryDuda
ICERM & Brown University

Antonio Macchia
Freie Universität Berlin

Kelly Maluccio
Texas A&M University

Madhusudan Manjunath
INDIAN INSTITUTE OF TECHNOLOGY BOMBAY

Hannah Markwig
Eberhard Karls University of Tübingen

Jesus MartinezGarcia
University of Essex

Mikhail Mazin
Kansas State University

Alex McDonough
Brown University

Hana Melánová
University of Vienna

Leonardo Mihalcea
Virginia Polytechnic Institute and State University

Kalina Mincheva
Yale University

Fatemeh Mohammadi
Ghent University

Sophie Morel
CNRS/ENS Lyon

Marc Moreno
University of Western Ontario

Jennifer Morse
University of Virginia

Philippe Nadeau
Institut Camille Jordan

Hiroshi Naruse
University of Yamanashi

Evangelos Nastas
SUNY

Gleb Nenashev
Brandeis University

Mounir Nisse
Xiamen University Malaysia

Roberto Pagaria
Alma Mater Studiorum Università di Bologna

Jianping Pan
University of California, Davis

Marta Panizzut
TU Berlin

Theodoros Stylianos Papazachariou
University of Essex

Beatriz Pascual Escudero
Universidad Carlos III de Madrid

Sam Payne
University of Texas at Austin

Nicolas Perrin
Versailles SaintQuentinenYvelines University

Nathan Pflueger
Amherst College

Viviane Pons
Université Paris Sud

Irem Portakal
OttovonGuerickeUniversitaet Magdeburg

Konstanze Rietsch
King's College London

Colleen Robichaux
University of Illinois at UrbanaChampaign

David Roe
Massachusetts Institute of Technology

Julian Rüth
none

Adriana Salerno
Bates College

Francisco Santos
University of Cantabria

AnnaLaura Sattelberger
Max Planck Institute for Mathematics in the Sciences

Mahrud Sayrafi
University of Minnesota

Hal Schenck
Auburn University

Anne Schilling
UC Davis

Daniel Schultz
Technische Universität Kaiserslautern

Oswaldo Sevilla
Centro de Investigación en Matemáticas, Guanajuato Mexico

Melissa ShermanBennett
UC Berkeley/Harvard

Farbod Shokrieh
University of Washington

Rob Silversmith
Northeastern University

Connor Simpson
University of Wisconsin  Madison

MirunaStefana Sorea
SISSA, Trieste

Frank Sottile
Texas A&M University

Sylvain Spitz
TU Berlin

Avery St. Dizier
Univeristy of Illinois at UrbanaChampaign

Bernd Sturmfels
MPI Leipzig

Changjian Su
University of Toronto

Nawaz Sultani
University of Michigan

Yuri Sulyma
Brown University

Mariel Supina
University of California, Berkeley

Pedro Tamaroff
Trinity College Dublin

Anna Tao
Brown University

Nicola Tarasca
Virginia Commonwealth University

Máté Telek
University of Copenhagen

Ayush Tewari
TU Berlin

Nicolas Thiéry
Université Paris Sud

Ling Hei Tsang
The Ohio State University

Jeremy Usatine
Brown University

Ravi Vakil
Stanford University

Paul Vater
Max Planck Institute for Mathematics in the Sciences

Lorenzo Vecchi
Alma Mater Studiorum  Università di Bologna

Emanuele Ventura
University of Bern

Weikun Wang
Southern University of Science and Technology

Andrzej Weber
Uniwersity of Warsaw

Anna Weigandt
University of Michigan

Lauren Williams
Harvard University

Rosa Winter
Max Planck Institute for Mathematics in the Sciences, Leipzig

Corey Wolfe
Tulane University

Cameron Wright
University of Washington

Weihong Xu
Rutgers

Ralph Xu
Syracuse University

Damir Yeliussizov
KazakhBritish Technical University

Alexander Yong
University of Illinois at UrbanaChampaign

Benjamin Young
University of Oregon

Chi Ho Yuen
Brown University

Claudia Yun
Brown University

Oguzhan Yürük
TU Berlin

Paul ZinnJustin
The University of Melbourne
Workshop Schedule
Monday, February 15, 2021

9:45  10:00 am ESTWelcomeVirtual
 Brendan Hassett, ICERM/Brown University

10:00  10:30 am ESTA brief tour of SageVirtual
 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 ESTRings and fields in SageVirtual
 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 ESTCoffee BreakVirtual

11:30 am  12:00 pm ESTCelestial mechanics via tropical geometry (gfan and Macaulay2)Virtual
 Anton Leykin, Georgia Tech

12:15  12:45 pm ESTFusionRings in Sage 9.2Virtual
 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 ESTLunch/Free TimeVirtual

2:00  3:00 pm ESTGathertown Welcome ReceptionReception  Virtual

3:00  4:00 pm ESTSage/Oscar Installation HelpTutorial  Virtual
Tuesday, February 16, 2021

9:00  9:45 am ESTGathertown Morning CoffeeCoffee Break  Virtual

10:00  10:30 am ESTOSCAR  The ProjectVirtual
 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 ESTOSCAR  Selected FeaturesVirtual
 Daniel Schultz, Technische Universität Kaiserslautern
Abstract
Introducing OSCAR, a new computer algebra system combining GAP, Polymake, Hecke and Singular.

11:15  11:30 am ESTCoffee BreakVirtual

11:30 am  12:00 pm ESTComputing the Newton polytope of a large discriminantVirtual
 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 Dequivalence classes of regular triangulations of the 3 dilated tetrahedron. The only known way to do this is to enumerate all regular triangulations of the 3dilated 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 ESTSome hybrid symbolicnumeric methods in algebraic geometryVirtual
 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 symbolicnumeric methods and applications in computational algebraic geometry.

1:00  2:00 pm ESTLunch/Free TimeVirtual

2:00  3:00 pm ESTProblem SessionVirtual

3:00  4:00 pm ESTContributing to Sage TutorialTutorial  Virtual
Wednesday, February 17, 2021

9:00  9:45 am ESTGathertown Morning CoffeeCoffee Break  Virtual

10:00  10:45 am ESTParallelization of Triangular Decompositions Design and implementation with the BPAS libraryVirtual
 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 "componentlevel" parallelization of triangular decompositions, our focus here, belongs to the class of dynamic irregular parallelism. Potential parallel speedup 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 componentlevel parallelization we combine different concurrency patterns: map, workpile, producerconsumer, 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 10.8times speed up on a 12core machine.

11:00  11:30 am ESTCoffee BreakVirtual

11:30 am  12:00 pm ESTRational integrals and periods with Sagemath and JuliaVirtual
 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 ESTGeneralized cohomology quotients of the symmetric functionsVirtual
 Darij Grinberg, Drexel University

1:00  2:00 pm ESTLunch/Free TimeVirtual

2:00  2:40 pm ESTLightning TalksVirtual
 Adam Afandi, Colorado State University
 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 ESTCoffee BreakVirtual

2:50  3:30 pm ESTLightning TalksVirtual
 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 UrbanaChampaign
 Mahrud Sayrafi, University of Minnesota
 Weihong Xu, Rutgers

3:30  4:30 pm ESTCode DemonstrationsTutorial  Virtual
Thursday, February 18, 2021

9:00  9:45 am ESTGathertown Morning CoffeeCoffee Break  Virtual

10:00  10:45 am ESTmsolve  A Library for Solving Polynomial SystemsVirtual
 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 stateoftheart. This is joint work with Jérémy Berthomieu, JeanCharles Faugère and Mohab Safey El Din from the PolSys Team at the Sorbonne Université in Paris.

11:00  11:30 am ESTParallelism in Algebraic Geometry  Examples with Singular and GPISpaceVirtual
 Anne FrühbisKrüger, University of Oldenburg
Abstract
I shall illustrate the use of the Singular  GPIspace interplay in some examples including a smoothness test, GITfans and desingularization.

11:45 am  12:45 pm ESTCoffee BreakVirtual

12:45  1:15 pm EST

1:30  2:30 pm ESTLunch/Free TimeVirtual

2:30  3:30 pm ESTProblem SessionVirtual

3:30  4:30 pm ESTCode DemonstrationsTutorial  Virtual
Friday, February 19, 2021

9:00  9:45 am ESTGathertown Morning CoffeeCoffee Break  Virtual

10:00  10:30 am ESTFactorizations into irreducibles and polytopesVirtual
 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 ESTComputational challenges for tropical del Pezzo surfacesVirtual
 María Angélica Cueto, Ohio State University
Abstract
A smooth degree d del Pezzo surface is obtained by blowing up the projective plane at (9d) 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 ESTCoffee BreakVirtual

11:30 am  12:00 pm ESTPresenting the multipolynomial bases packageVirtual
 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

1:00  2:00 pm ESTLunch/Free TimeVirtual

2:00  3:00 pm ESTGathertown Closing ReceptionReception  Virtual
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