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Kailash Misra, NC State, Affine Lie Algebras and Crystals

September 24, 2021 | 3:00 pm - 4:00 pm EDT

Affine Lie algebras, also sometimes called current algebras, are infinite-dimensional analogs of finite-dimensional semisimple Lie algebras. The representation theory of affine Lie algebras has applications in many areas of mathematics (number theory, combinatorics, group theory, geometry, topology, etc.) and physics (conformal field theory, integrable systems, statistical mechanics, etc.). To study the combinatorial properties of affine Lie algebra representations, Kashiwara and Lusztig independently introduced combinatorial objects called crystals associated with each irreducible integrable representation of an affine Lie algebra. In 1992, Misra et al. introduced perfect crystals to give explicit realizations of the corresponding affine crystals. In 2000, Berenstein and Kazhdan introduced the notion of a geometric crystal whose ultra-discretization becomes an algebraic crystal. In this talk we will survey some of these developments and state some recent results.

Kailash Misra received his Ph.D. in Mathematics from Rutgers University, NJ, in 1982. He had postdoctoral appointments at University of Virginia during 1982–1984 and University of Wisconsin, Madison, during 1984–1986. Dr. Misra joined NCSU in Fall 1986 and was promoted to Associate Professor in 1991 and Full Professor in 1995. He received the NCSU Outstanding Teacher Award in 2004 and became a Fellow of the American Mathematical Society in 2014. Dr. Misra’s current research interests are representation theory of Kac–Moody Lie algebras, Quantum groups, and related topics.

Contact the host, Dmitry Zenkov for the zoom link.

Details

Date:
September 24, 2021
Time:
3:00 pm - 4:00 pm EDT
Event Category:

Venue

SAS 1102