NSF/CBMS Regional Conference on Higher Representation Theory-June 19-23, 2014

North Carolina State University, Raleigh NC

Investigators

Abstract

This project will support a five-day CBMS conference on "Higher representation theory of Kac-Moody algebras" at North Carolina State University in June 2014 with Raphael Rouquier as the principal speaker. The theory of Kac-Moody Lie algebras and their quantum analogs is a timely topic with various applications to other branches of mathematics and theoretical physics. Major developments have been focused on the categorification program which realizes key algebraic structures, such as canonical bases, in terms of category of modules based on combinatorial, algebraic or geometric structures. Categorification can provide deeper understanding of the original algebraic structures and obtain new structures. In categorification of quantum enveloping algebras, Khovanov-Lauda and Rouquier independently introduced the KLR algebra. As one of the inventors and a leading practitioner in this field, Professor Rouquier will give ten lectures on the subject which aim to introduce workshop participants, including graduate students, to current research and chart possible future directions. Prof. Rouquier will also write up a monograph of the CBMS lectures after the conference. The conference expects to gather about 40 participants. An additional five speakers are invited to assist Professor Rouquier's lectures and to talk about categorification and higher representation theory. The conference will encourage participation from women, minorities, and persons with disabilities.