SageDays@ICERM: Combinatorics and Representation Theory
(July 23 - 27, 2018)
polytope for the crystal B(∞) in type C2, generated using SageMath.
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.