Friedrich-Hirzebruch-Kolloquium: Prof. Dr. Don Zagier (Max-Planck-Institut Bonn): Modular forms and their appearances in physics
Thursday, 21.12.2017 16:00 im Raum M5
Modular forms, which are among the most beautiful and important objects
in number theory, are functions of a complex variable with an infinite
group of symmetries and that also often lead via their Fourier expansions
to interesting arithmetical functions. They have important applications
in many parts of pure mathematics, ranging from Diophantine equations
to differential geometry to coding theory, but in recent years also
many different kinds of applications in mathematical physics. In the
talk, which assumes no prior knowledge, I will try to explain what modular
forms (and a more recent variant called "mock modular forms") are, with
explicit examples, and then describe two or three of their most surprising
recent appearances in physics: in connection with the string theory of
black holes; in connection with the various brands of "moonshine"
(the "monstrous" version discovered in the 80's and the "Mathieu"
and "umbral" versions discovered recently); and in connection with
"Nahm's conjecture", which came originally from conformal field
theory and has now been proved (by Calegari, Garoufalidis and
myself) and discovered to be related to quantum invariants of knots.