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Organizing Committee
Rutgers University
Technische Universität Kaiserslautern
Saint Louis University
TU Berlin & MPI Leipzig
none
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.
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.
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Workshop Schedule
Monday, February 15, 2021
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
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.
