Meromorphic Connections

The Geometry working seminar in Fall 2013 is devoted to the theory of meromorphic connections. A goal is to understand its application to wall-crossing formulae for Donaldson-Thomas invariants via isomonodromic deformations. Hopefully, we will cover other aspects of the general theory --depending on the taste of the participants-- as: moduli of meromorphic connections, wild non abelian Hodge theory, Stokes grupoids ...

For the application to wall-crossing we will follow the references

1. "Stability conditions and Stokes factors" by T. Bridgeland and V. Toledano Laredo.

2. "Stokes factors and multilogarithms" by T. Bridgeland and V. Toledano Laredo.

For the general theory of meromorphic connections we will follow the work of Boalch (among others), starting with

3. "Symplectic manifolds and isomonodromic deformations" by P. Boalch.

4. "G-bundles, isomonodromy and quantum Weyl groups" by P. Boalch.

Seminars:

25 September, Ben Davison "Introduction to cohomological Hall algebras".

2 October, Mario Garcia-Fernandez "Meromorphic connections and wall-crossing: an overview".

9 October, Szilard Szabo "Moduli spaces of logarithmic connections on curves and Hilbert schemes".

16 October, Mario Garcia-Fernandez "G-valued Stokes data: an example".

30 October, Michael Wong "Isomonodromic deformation".

6 November, Klaus-Dieter Semmler "Hyperelliptic Riemann Surfaces and Hyperbolic Polygons".

13 November, Danielle Boccalini "Hilb(T*C) and Higgs bundles" and Szilard Szabo "Parallel transport for Fuchsian connections" .

20 November, Szilard Szabo "Parallel transport for Fuchsian connections and the Laplace transform" .

4 December, Ben Davison "Ringel-Hall algebras and irregular connections".

11 December, Martin Mereb "A formula to trace a trace formula".

18 December, Szilard Szabo "Stokes matrices and multilogarithms" and Mario Garcia-Fernandez "The semiclassical limit of the Stokes map".