Kommende Vorträge

For zoom details contact Christian Kaiser (kaiser@mpim-bonn.mpg.de)

Abstract:

Determination of modular forms is one of the fundamental and interesting
problems in number theory. It is known that if the Hecke eigenvalues of two
newforms agree for all but finitely many primes, then both the forms are
the same. In other words, the set of Hecke eigenvalues at primes determine
the newform uniquely and this result is known as the multiplicity one
theorem. In the case of Siegel cuspidal eigenforms of degree two, the
multiplicity one theorem has been proved only recently in 2018 by Schmidt.

The theory of Hall algebras has known many spectacular developments and applications since the discovery by Ringel of their connection with quantum groups. One important object arising naturally in the study of Hall algebras is the integration map defined by Reineke, which allows to produce certain celebrated wall-crossing identities. In this talk I will first focus on the Dynkin case and show how the integration map can be interpreted in a natural way via the representation theory of quantum affine algebras.