# 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.