Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Status Confirmed
Seminar Series MATH-IHES
Subjects math
Date Monday 2 October 2023
Time 10:30
Institute IHES
Seminar Room Amphithéâtre Léon Motchane
Speaker's Last Name Kumar
Speaker's First Name Shrawan
Speaker's Email Address
Speaker's Institution University of North Carolina, Chapel Hill & IHES
Title Verlinde Dimension Formula for the Space of Conformal Blocks and the moduli of G-bundles
Abstract Let G be a simply-connected complex simple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable formula to calculate the dimension of the space of generalized theta functions, which is by definition the space of global sections of a determinant line bundle. This space is also identified with the space of conformal blocks arising in Conformal Field Theory, which is by definition the space of coinvariants in integrable highest weight modules of affine Kac-Moody Lie algebras. Various works notably by Tsuchiya-Ueno-Yamada, Kumar-Narasimhan-Ramanathan, Faltings, Beauville-Laszlo, Sorger and Teleman culminated into a proof of the Verlinde formula. The main aim of this talk is to give a basic outline of the proof of this formula derived from the Propogation of Vacua and the Factorization Theorem among others. The proof requires techniques from algebraic geometry, geometric invariant theory, representation theory of affine Kac-Moody Lie algebras, topology, and Lie algebra cohomology. Some basic knowledge of algebraic geometry and representation theory of semisimple Lie algebras will be helpful; but not required. This lecture should be suitable for any one interested in interaction between algebraic geometry, representation theory, topology and mathematical physics.
arXiv Preprint Number

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