Conference: Southeastern Lie Theory Workshop Series

North Carolina State University, Raleigh NC

Investigators

Abstract

This project supports participation in two workshops: "Combinatorial Representation Theory of Algebras and Applications" (May 12-14, 2023: North Carolina State University) and "Quantum Groups, Quantum Symmetric Pairs and their Categorifications" (March 1-3, 2024, University of Virginia) in the Southeastern Lie Theory Workshop Series. The Southeast Lie Theory Consortium and Workshop Series will continue to stimulate and enhance regional research collaboration in Lie theory and representation theory in the Southeastern United State. Featured expository talks at the workshops by leading researchers will provide an avenue for graduate students and early-career researchers to enhance their research programs. The opportunities for mathematical interactions and mentorship during the conferences will foster a strong regional tradition of research and education. The proposed workshops are broadly concerned with the representation theory of Lie algebras, quantum groups, and related algebraic structures. These topics have numerous connections to theoretical physics, number theory, algebraic geometry, and other disciplines. Research in these fields involves the study of a broad range of algebraic, combinatorial, or categorical objects, a sampling of which includes: quantized enveloping algebras, quantum function algebras, Kac--Moody Lie algebras, Hecke algebras, canonical bases and crystal bases, vertex operator algebras, Hall algebras, quivers, cluster algebras, Hopf algebras, and Khovanov-Lauda-Rouquier algebras. In general, the representation theory of quantized Kac--Moody Lie algebras and its accompanying categorical and geometric developments has taken on a significant role not only within Lie theory but also in other areas of mathematics and physics such as combinatorics, group theory, number theory, integrable systems, low-dimensional topology and conformal field theory. The workshop series website is https://www.math.lsu.edu/~pramod/selie/. The website for the May 2023 Workshop is https://sites.google.com/ncsu.edu/selieworkshop2023. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.