School of Mathematics Seminars and Lectures
Mock Modular Forms and Quantum Black Holes
by Prof. Atish Dabholkar (CNRS, University of Paris, France)
Friday, March 2, 2012
from
to
(Asia/Kolkata)
at Colaba Campus ( Maths. Seminar Room A-369 )
at Colaba Campus ( Maths. Seminar Room A-369 )
Description |
I will explain the relation between mermorphic Jacobi forms, mock Jacobi forms, and the wall-crossing phenomenon in certain problems in enumerative geometry along with the physics context of quantum black holes in which they arise. Analysis of the generating functions for quantum degeneracies of a class of black holes in string theory leads to an infinite family of meromorphic Jacobi forms. This family (and another related one) in turn furnishes a list of examples of mock modular and mock Jacobi forms. This list contains many known mock modular forms including the mock theta functions of Ramanujan, the generating function of Hurwitz-Kronecker class numbers, the mock modular form conjecturally related to the Mathieu group M24, as well as an infinite number of new examples. |