Research Group:

## Geometry of Character Varieties

The course will cover some of the work with Hausel and Letellier on the subject. Basic tools on finite fields, Weil conjectures, group representations and symmetric functions will be discussed as needed.

## Algebraic Geometry

## Research topics

- Construction of virtual classes and their use to define enumerative invariants; properties of the invariants and methods for their computations. Extension to orbifolds/smooth Deligne-Mumford algebraic stacks of constructions for manifolds, in particular Gromov-Witten invariants and Chen-Ruan cohomology.
- Moduli spaces, such as moduli of (decorated) sheaves (including principal bundles, Higgs bundles, coherent systems, instantons), stable maps, varieties and Hilbert and Quot schemes. Deformation theory and additional structures such as algebraic stacks and dg-schemes. Hitchin-Kobayashi correspondence.
- Applications to and relations with topological field theories and string theory.
- Equivariant cohomology and localization formulas.