Organizers: Murad Alim
Dates (organizational meeting/introduction on April 4th 2022, first seminar on April 11th, 2022):
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 nonperturbative 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.
Content and literature: hereSessions this term:
Date 
Speaker 
Topic 
Room 
04.04.2022 
Murad Alim 
Intoduction to the topic 
Geom 431 
11.04.2022 
Murad Alim 
Borel resummation for Euler equation and Gamma function 
Geom 431 
25.04.2022 
Daniel Bryan 
Linear differential systems (Chapter 1 of MS book) 
Geom 431 
02.05.2022 
Daniel Bryan 
Linear differential systems (Chapter 1 of MS book)

Geom 431 
16.05.2022 
Can Turan 
Introduction to differential Galois theory  Geom 431 
30.05.2022 
Can Turan and Paul Veltman 
Introduction to differential Galois theory II  Geom 431 
13.06.2022 
Deniz Bozkurt 
Inverse Problems  Geom 431 
20.06.2022 
Ivan/Tobias 
The Riemann Hilbert Problem  Geom 431 
27.06.2022 
Andres Gomes 
Vector Bundles and Connections  Geom 431 
04.07.2022 
Ivan/Tobias 
The Riemann Hilbert Problem  Geom 431 
11.07.2022 
tbd 
BorelLaplace Summation  Geom 431 