Events

In this talk I will consider the Maxwell-Schrödinger equations in the Coulomb gauge describing the interaction of extended fermions with their self-generated electromagnetic field. In the first part, I will explain how these equations heuristically emerge from non-relativistic quantum electrodynamics in a mean-field limit of many fermions. The second part is dedicated to the rigorous derivation of the Vlasov-Maxwell dynamics from the Maxwell-Schrödinger equations with extended charges in the semiclassical regime. The talk is based on a joint work with Chiara Saffirio.

Donaldson-Thomas (DT) and Pandharipande-Thomas (PT) invariants are two curve counting invariants for 3-folds. In the Calabi-Yau case, a correspondence between the numerical DT and PT invariants has been conjectured by Pandharipande and Thomas and proven by Bridgeland and Toda using wall-crossing. For equivariant K-theoretically refined invariants, the DT/PT correspondence reduces to a DT/PT correspondence of equivariant K-theoretic vertices. In this talk I will explain our proof of the equivariant K-theoretic DT/PT vertex correspondence using a K-theoretic version of Joyce's wall-crossing setup. An important technical tool is the construction of a symmetized pullback of a symmetric perfect obstruction theory on the orginial DT and PT moduli stacks to a symmetric almost perfect obstruction theory on auxiliary moduli stacks. This is joint work with Henry Liu and Nick Kuhn.