Organizing Committee
Abstract

SageMath (sometimes Sage for short) is an open-source, general purpose mathematical software based on the Python programming language. It was created in 2005 by William Stein as a viable alternative to commercial software with an active and established community. SageMath has a broad library of functions useful to mathematicians in many fields, including combinatorics and representation theory. The welcoming and engaged community of users and contributors helps to create an environment of collaboration in both software development and mathematical research, leading to SageMath being cited in over 300 papers.

The study of the representation theories of certain algebras (e.g., Lie algebras, Hecke algebras, Khovanov–Lauda–Rouquier (KLR) algebras, quantum groups, etc.) also amounts to understanding the associated combinatorics. This has exposed deep connections between the associated representation theory and other areas of mathematics and physics. However, there are still areas in which development is urgently needed; for example, representation theory of Lie superalgebras, Borcherds (or generalized Kac–Moody) algebras and their representations, KLR algebras, etc.

The primary goal of this workshop is to expand and improve the combinatorics, algebra, and representation theory in SageMath by increasing the user base and encouraging users to contribute their own code. Thus, similar to previous SageDays, this workshop is open to all levels of experience with SageMath: from those who want to discover SageMath to experienced developers.

The workshop will partially consist of talks, presentations, and active demonstrations on some of the relevant mathematical topics, using SageMath, and coding within SageMath. The rest of the workshop will be devoted to coding sprints, time where people can work (either individually or in groups) on code or applying SageMath. The nature of the talks on the underlying mathematics will vary from introductory to specialized and will be aimed at the interests of those participating. Similarly, the presentations on SageMath will include introductory tutorials and extend to development in SageMath.

Image for "SageDays@ICERM: Combinatorics and Representation Theory "
Animation of how the crystal operators behave in the MV polytope for the crystal B(∞) in type C2, generated using SageMath.

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, July 23, 2018
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTIntroduction to Sage - Ben Salisbury, Central Michigan University11th Floor Lecture Hall 
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTComputing huge subspaces of polynomials- Symmetries to the rescue - Nicolas Thiéry, LRI, Université Paris Sud11th Floor Lecture Hall
11:30 - 12:15pm EDTLie Superalgebras and Sage - Dan Bump, Stanford University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTThe Chinta-Gunnells action and sums over highest weight crystals - Anna Puskás, University of Massachusetts, Amherst11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTCharacterization of queer super crystals - Anne Schilling, University of California, Davis11th Floor Lecture Hall
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, July 24, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTRowmotion and toggle dynamics in Sage - Jessica Striker, North Dakota State University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTPaths to understanding rowmotion in products of chains - Tom Roby, University of Connecticut11th Floor Lecture Hall
11:30 - 12:15pm EDTFull Twist Presentations - Nathan Williams, University of Texas at Dallas11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTThe Rise-Contact involution on Tamari intervals - Viviane Pons, Université Paris-Sud11th Floor Lecture Hall
3:30 - 4:15pm EDTToward double affine flag varieties and Grassmannians - Dinakar Muthiah, University of Massachusetts, Amherst11th Floor Lecture Hall
4:30 - 5:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Wednesday, July 25, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTThe quantum Heisenberg category and centers of Hecke algebras - Jonathan Brundan, University of Oregon11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTFinite order automorphisms on Borcherds algebras - Elizabeth Jurisich, The College of Charleston11th Floor Lecture Hall
11:30 - 12:15pm EDTWeb bases for rings of SL_3 invariants - Hugh Thomas, Université du Québec à Montréal11th Floor Lecture Hall
12:30 - 12:40pm EDTGroup Photo11th Floor Lecture Hall 
12:40 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTA construction of the affine VW supercategory - Mee Seong Im, United States Military Academy11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTCanonical Bases Elements in Symmetric Kashiwara Crystals of Type A - Mary Schaps, Bar-Ilan University11th Floor Lecture Hall
5:00 - 5:15pm EDTExternal Littelman Paths For Crystals Of Type A, rank 2 - Ola Amara Omari, Bar-Ilan University11th Floor Lecture Hall
Thursday, July 26, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTGeneralized Jucys-Murphy elementes and canonical idempotents in towers of algebras - Aaron Lauve, Loyola University Chicago11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTBack-stable Schubert calculus - Mark Shimozono, Virginia Tech11th Floor Lecture Hall
11:30 - 12:15pm EDTUnitary friezes from affine quivers - Emily Gunawan, University of Connecticut11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 2:45pm EDTShifted Symmetric Functions from Heisenberg Categories - Can Ozan Oguz, University of Southern California11th Floor Lecture Hall
2:45 - 3:00pm EDTPacked Words and WQSym basis - Hugo Mlodecki, Université Paris-Sud11th Floor Lecture Hall 
3:00 - 3:15pm EDTChained Permutations - Dylan Heuer, North Dakota State University11th Floor Lecture Hall
3:15 - 3:30pm EDTCombinatorics + Algebra -> Differential Geometry - Vit Tucek, University of Zagreb11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTCoding Sprints11th Floor Lecture Hall 
Friday, July 27, 2018
TimeEventLocationMaterials
9:00 - 9:45am EDTCoding Sprints11th Floor Lecture Hall 
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTUse of Sage in my Research - Kyu-Hwan Lee, University of Connecticut11th Floor Lecture Hall
11:30 - 12:15pm EDTCoding Sprints11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTPresentations of the week's work - Active Participants11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTCoding Sprints11th Floor Lecture Hall 

Lecture Videos

Use of Sage in my Research

Kyu-Hwan Lee
University of Connecticut
July 27, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Unitary friezes from affine quivers

Emily Gunawan
University of Connecticut
July 26, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Back-stable Schubert calculus

Mark Shimozono
Virginia Tech
July 26, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Generalized Jucys-Murphy elementes and canonical idempotents in towers of algebras

Aaron Lauve
Loyola University, Chicago
July 26, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract     Slides

External Littelman Paths For Crystals Of Type A, rank 2

Ola Amara Omari
Bar-Ilan University
July 25, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Canonical Bases Elements in Symmetric Kashiwara Crystals of Type A

Mary Schaps
Bar-Ilan University
July 25, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Web bases for rings of SL_3 invariants

Hugh Thomas
Université Québec a Montréal
July 25, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Finite order automorphisms on Borcherds algebras

Elizabeth Jurisich
University of Charleston
July 25, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

The quantum Heisenberg category and centers of Hecke algebras

Jon Brundan
University of Oregon
July 25, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract     Slides

Toward double affine flag varieties and Grassmannians

Dinakar Muthiah
University of Massachusetts - Amherst
July 24, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

The Rise-Contact involution on Tamari intervals

Viviane Pons
Université Paris Sud
July 24, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Independence Posets

Nathan Williams
University of Texas at Dallas
July 24, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Paths to understanding rowmotion in products of chains

Tom Roby
University of Connecticut
July 24, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract     Slides

Rowmotion and toggle dynamics in Sage

Jessica Striker
North Dakota State University
July 24, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Characterization of queer super crystals

Anne Schilling
University of California, Davis
July 23, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract     Slides

The Chinta-Gunnells action and sums over highest weight crystals

Anna Puskás
University of Massachusetts, Amherst
July 23, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract     Slides

Lie Superalgebras and Sage

Daniel Bump
Stanford University
July 23, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract     Slides

Computing huge subspaces of polynomials- Symmetries to the rescue

Nicolas Thiéry
Université Paris Sud
July 23, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play     Abstract

Introduction to Sage

Ben Salisbury
Central Michigan University
July 23, 2018
SageDays@ICERM: Combinatorics and Representation Theory
Play