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:
| DATE and TIME | TITLE | SPEAKER | ABSTRACT |
|---|---|---|---|
| Tuesday 5/30 at 10:30am in room 313 | Symplectic structures on moduli of Stokes data | Tony Pantev | Abstract |
| Wednesday 5/31 at 10:30am in room 313 | Geometry and Borel Summability of Exact WKB Solutions | mini-course Nikita Nikolaev | Abstract |
| Thursday 6/1 at 10:30am in room 313 | Geometry and Borel Summability of Exact WKB Solutions | mini-course Nikita Nikolaev | Abstract |
| Friday 6/2 at 10:30am in room 313 | A functorial Riemann-Hilbert correspondence | Andrea D’Angolo | Abstract |
| Monday 6/5 at 10:30am in room 103 | Stokes phenomena, Poisson-Lie groups and quantum groups | Valerio Toledano-Laredo | Abstract |
| Tuesday 6/6 at 10:30am in room 103 | Wall-crossing in exact WKB and hyperkahler geometry | Andrew Neitzke | |
| Wednesday 6/7 at 10:30am in room 103 | Stokes phenomena, coalescence of poles and triangulations of Riemann surfaces | Marta Mazzocco | Abstract |
| Thursday 6/8 at 10:30am in room 103 | The derived moduli stack of logarithmic flat connections | Francis Bischoff | Abstract |
| Monday 6/12 at 10:30 in room 103 | Deligne-Lusztig varieties as moduli spaces of sheaves | David Treumann | Abstract |
| Tuesday 6/13 at 10:30 in room 103 | Topological recursion, WKB analysis, and (uncoupled) BPS structures | Omar Kidwai | Abstract |
| Wednesday 6/14 at 10:30 in room 103 | Vladimir Fock (to be confirmed) | ||
| Thursday 6/15 at 10:30 in room 103 | Marked singularities, their moduli spaces, distinguished bases and Stokes regions. | Claus Hertling | Abstract |
| Tuesday 6/20 at 10:30 in room 103 | The Chromatic Lagrangian: Wavefunctions and Open Gromov-Witten Conjectures | Eric Zaslow | Abstract |
| Wednesday 6/21 at 10:30 in room 103 | First Steps in Global Lie Theory: wild Riemann surfaces, their character varieties and topological symplectic structures | Philip Boalch | Abstract |
| Thursday 6/22 at 10:30 in room 103 | Irregular connections, Stokes geometry, and WKB analysis | Yan Zhou | Abstract |
| Friday 6/23 at 10:30 in room 103 | Isomonodromy times and conformal blocks | Gabriele Rembado | Abstract |
