The Stokes Phenomenon and its Applications in Mathematics and Physics: May 22 – June 30, 2023

Participant List

Organized by: Anton Alekseev (University of Geneva) Marco Gualtieri (Univ. of Toronto) Xiaomeng Xu (Peking University)

When a system of differential equations has an irregular singularity, such as a pole of order two or higher, a solution may fail to have a well-defined asymptotic expansion at the singular locus. Instead, there is a collection of angular sectors surrounding the singular locus, in each of which an asymptotic expansion is defined. The existence of such sectorial asymptotic expansions is what is called the “Stokes phenomenon”. The Stokes phenomenon has found remarkable applications in different areas of mathematics and physics, such as in cohomological field theory, the study of Bridgeland stability conditions, noncommutative Hodge theory, cluster algebras, quantum groups and so on. In particular, the Stokes phenomenon is the essential ingredient in an irregular version of the Riemann-Hilbert correspondence, where the moduli space of differential equations with irregular singularities is described in terms of its associated generalized monodromy data (Stokes matrices). The geometric nature of this Riemann–Hilbert map from the moduli space of differential equations or “de Rham moduli space” to the space of Stokes matrices or “Betti moduli space” has been intensively studied for the past twenty years. Moreover, the crucial role of the Stokes phenomenon in the study of representation theory and integrable systems is only beginning to emerge. The overall goal of the program is to bring together specialists in the above mentioned topics to exchange ideas and perspectives, with the aim of breaking new ground in these related fields of physics and mathematics.

Schedule of Program Talks:  *All talks will be held in room 313 unless otherwise noted below

Tuesday 5/30 at 10:30am Symplectic structures on moduli of Stokes data Tony Pantev Abstract
Wednesday 5/31 at 10:30am Geometry and Borel Summability of Exact WKB Solutions mini-course Nikita Nikolaev Abstract
Thursday 6/1 at 10:30am Geometry and Borel Summability of Exact WKB Solutions mini-course Nikita Nikolaev Abstract
Friday 6/2 at 10:30am A functorial Riemann-Hilbert correspondence Andrea D’Angolo Abstract
Monday 6/5 at 10:30am  Stokes phenomena, Poisson-Lie groups and quantum groups Valerio Toledano-Laredo Abstract
Tuesday 6/6 at 10:30am Wall-crossing in exact WKB and hyperkahler geometry Andrew Neitzke  
Wednesday 6/7 at 10:30am Stokes phenomena, coalescence of poles and triangulations of Riemann surfaces Marta Mazzocco Abstract
Thursday 6/8 at 10:30am The derived moduli stack of logarithmic flat connections Francis Bischoff Abstract