Research Talks

Xin Jin

Mirror symmetry for the affine Toda systems

 I'll present recent work on mirror symmetry for the affine Toda systems, which can be viewed as a Betti Geometric Langlands correspondence in the wild setting. More explicitly, we realize the affine Toda system (associated to a complex semisimple group) as a moduli space of Higgs bundles on P^1 with certain automorphic data, and the dual side is the group version of the universal centralizer (associated to the dual group), which is a wild character variety. We show that the wrapped Fukaya category of the former is equivalent to the dg-category of coherent sheaves of the latter. This is joint work with Zhiwei Yun.

Qiongling Li

 Harmonic metrics on Higgs bundles over non-compact surfaces

For a Higgs bundle over a compact Riemann surface of genus at least 2, the Hitchin-Kobayashi correspondence says the existence of a harmonic metric is equivalent to the polystability of the Higgs bundle. In this talk, we discuss some recent progress on the existence and uniqueness of harmonic metrics on Higgs bundles over general non-compact Riemann surfaces. This is joint work with Takuro Mochizuki.

Claude Sabbah

TBA

Annette Werner

TBA