Research Seminar on String Mathematics, Summer 2022, Monodromy and Resurgence

Organizers: Murad Alim

Dates (organizational meeting/introduction on April 4th 2022, first seminar on April 11th, 2022):

• Monday, 14:15-15:45 in Geomatikum 431.

Description:

The topic of the research seminar for string mathematics for the summer term 2022 is Monodromy and resurgence. It is open to anyone interested in research questions around this topic. It will consist of several talks given by the participants of the seminar following some suggested literature and may include research talks given by external invited speakers.

Resurgence refers to the mathematical treatment of divergent formal power series using the Borel transform and the study of the Borel summability of the Borel transform and the associated Stokes phenomena. Divergent power series are ubiquitous in quantum mechanics, quantum field- and string theories. These are typically obtained using a perturbative formulation of the theory or of its correlation- and partition functions. The divergence of the obtained formal series in the expansion parameter signals missing contributions from non-perturbative effects which can be made precise using the methods of resurgence. Within mathematics resurgent power series are often found as solutions of differential equations near irregular singular points, the Borel transform and summation also allows here to recover analytic functions defined over larger domains from the asymptotic expansion.

The aim of this seminar is to understand the mathematical structures behind the ideas of resurgence as well as to discuss some of its applications/appearances in exact WKB, QFT and string theory.

Sessions this term: