“Refined invariants in Moduli Theory”
Lunedì 10 Giugno 2024, ore 13:00 - Aula 1BC45 - Sergej Monavari (École Polytechnique Fédérale de Lausanne)
Abstract
Intersection theory provides a classical way to extract numerical invariants of smooth projective varieties. We give a gentle introduction on how torus actions provide a natural refinement of intersection theory which produces representation-theoretic invariants of quasi-projective varieties. As a concrete example, we explain how to extract meaningful invariants from the Quot schemes of the affine three-space, which are rather singular moduli spaces of sheaves. Finally, by packaging all these invariants into generating series, we obtain closed combinatorial formulas, which solve a series of conjectures originally proposed in Topological String Theory.
This is based on joint work with N. Fasola and A. Ricolfi.
