220621 Sergej Monavari

A classical way to produce invariants is through Intersection Theory, usually on a smooth projective variety. We give a gentle introduction on how to use torus actions to refine invariants in several directions, in particular in K-theory, and on how to weaken smoothness and properness assumptions. As a concrete example, we explain how to extract meaningful invariants from the moduli space of zero-dimensional quotients of a locally free sheaf on a toric variety, and illustrate various closed formulas for different flavours of “higher rank Donaldson-Thomas invariants of points”, which solve a series of conjectures proposed in String Theory. This is based on joint work with N. Fasola and A. Ricolfi.