OIST Representation Theory Seminar

Travis Scrimshaw, Hokkaido University

Title: An Overview of Kirillov-Reshtikhin Modules and Crystals

Abstract: Kirillov-Reshetikhin (KR) modules are an important class of finite dimensional representations associated to an affine Lie algebra and the associated Yangian and quantum group. KR modules are known to appear in many integrable systems and govern the dynamics. In this talk, we will give an overview of the role KR modules play in the category of finite dimensional representations, R-matrices and the fusion construction, their (conjectural) crystal bases, and how they relate to Demazure modules. In particular, we will focus on how to construct their crystal bases combinatorially and the different types of character theories. As time permits, we will discuss some of the relations with (quantum) integrable systems.

Profile: Travis Scrimshaw is an assistant professor at Hokkaido University whose research focuses on combinatorial aspects of representation theory, integrable systems, and stochastic processes. He is an active developer of the open-source mathematical software SageMath. He received his PhD in 2015 at the University of California, Davis under the supervision of Anne Schilling. Afterwards, he did postdocs at the University of Minnesota, the University of Queensland, and Osaka Metropolitan University (JSPS postdoc).

Travis is currently visiting OIST through the Theoretical Sciences Visiting Program (TSVP)