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 multi-variate 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 in-person 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 California-Davis
-
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
-
Pierre-Emmanuel Chaput
université de Lorraine
-
Anastasia Chavez
University of California, Davis
-
Sunita Chepuri
University of Michigan
-
Man-Wai 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 Frühbis-Krüger
University of Oldenburg
-
William Fulton
University of Michigan
-
Nir Gadish
MIT
-
Pavel Galashin
University of California, Los Angeles
-
Marina Garrote-López
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
Daegu-Gyeongbuk 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 Paris-Saclay
-
Anton Leykin
Georgia Tech
-
Shiyue Li
Brown University
-
David Lowry-Duda
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 Martinez-Garcia
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 Saint-Quentin-en-Yvelines University
-
Nathan Pflueger
Amherst College
-
Viviane Pons
Université Paris Sud
-
Irem Portakal
Otto-von-Guericke-Universitaet Magdeburg
-
Konstanze Rietsch
King's College London
-
Colleen Robichaux
University of Illinois at Urbana-Champaign
-
David Roe
Massachusetts Institute of Technology
-
Julian Rüth
none
-
Adriana Salerno
Bates College
-
Francisco Santos
University of Cantabria
-
Anna-Laura 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 Sherman-Bennett
UC Berkeley/Harvard
-
Farbod Shokrieh
University of Washington
-
Rob Silversmith
Northeastern University
-
Connor Simpson
University of Wisconsin -- Madison
-
Miruna-Stefana Sorea
SISSA, Trieste
-
Frank Sottile
Texas A&M University
-
Sylvain Spitz
TU Berlin
-
Avery St. Dizier
Univeristy of Illinois at Urbana-Champaign
-
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
Kazakh-British Technical University
-
Alexander Yong
University of Illinois at Urbana-Champaign
-
Benjamin Young
University of Oregon
-
Chi Ho Yuen
Brown University
-
Claudia Yun
Brown University
-
Oguzhan Yürük
TU Berlin
-
Paul Zinn-Justin
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 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 ESTSome hybrid symbolic-numeric 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 symbolic-numeric 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 "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 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 Urbana-Champaign
- 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 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 ESTParallelism in Algebraic Geometry - Examples with Singular and GPI-SpaceVirtual
- 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 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 (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 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
All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).
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