The geometric Langlands program can be described in a natural way by compactifying on a
Riemann surface C a twisted version of N= 4 super Yang-Mills theory in four dimensions …

We prove the P=W conjecture for GL_n for all ranks n and curves of arbitrary genus g≥2.
The proof combines a strong perversity result on tautological classes with the curious Hard …

We reformulate the Ω-deformation of four-dimensional gauge theory in a way that is valid
away from fixed points of the associated group action. We use this reformulation together …

We calculate the E-polynomials of certain twisted GL (n, ℂ)-character varieties M_n of
Riemann surfaces by counting points over finite fields using the character table of the finite …

These lecture notes give an overview of recent results in geometric Langlands
correspondence which may yield applications to quantum field theory. It has long been …

We show that the Hitchin integrable system for a simple complex Lie group $ G $ is dual to
the Hitchin system for the Langlands dual group $\lan {G} $. In particular, the general fiber of …

For G= GL 2, PGL 2, SL 2 we prove that the perverse filtration associated with the Hitchin
map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a …

A bstract We introduce a new wall-crossing formula which combines and generalizes the
Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems …

We discuss the relation between Liouville theory and the Hitchin integrable system, which
can be seen in two ways as a two step process involving quantization and hyperkähler …

We take another approach to Hitchin's strategy of computing the cohomology of moduli
spaces of Higgs bundles by localization with respect to the circle action. Our computation is …