This semester the Amsterdam Math-Physics Colloquium will take place on Friday 7 June, and the speakers will be Don Zagier (MPI Bonn) and Boris Pioline (UPMC Paris).
09.30- 10.00 coffee/tea
10.00- 11.00 Prof. Don Zagier
11.00- 11.30 coffee/tea
11.30- 12.30 Prof. Boris Pioline
Prof. Don Zagier
Title: Knot q-series and modularity
Prof. Boris Pioline
Title: Schwarzschild meets Ramanujan: From quantum black holes to mock modular forms
Abstract: While black holes are by now firmly established as astrophysical objects, they continue to raise conceptual puzzles for theorists -- one of them being the microscopic origin of the Bekenstein-Hawking entropy. An important breakthrough was achieved almost 25 years ago for supersymmetric black holes in string theory, whose micro-states can be described by D-brane bound states and counted (with signs) exactly. In the simplest case with maximal supersymmetry, the generating functions of exact degeneracies turns out to be a weak modular form, familiar from 19th century mathematics. In cases with reduced supersymmetry, the counting must take into account wall-crossing phenomena, whereby black hole bound states may form or decay depending on the values of the scalar fields at spatial infinity. Recent work has shown that generating functions of exact degeneracies of single-centered black holes are no longer exactly modular. Rather, they belong to the class of `mock modular forms', which generalizes the 'mock theta functions' introduced by Ramanujan just before his premature death in 1920. I will attempt to review these developments for non-experts, and convey some of the excitement which has happened over the last few years at this juncture between physics and mathematics.
Science Park 904, room C1.112