Microformal geometry, Batalin-Vilkovisky algebras and Fourier integral operators

Dr Theodore Voronov (The University of Manchester)

Frank Adams Room 1,

I will recall the notion of "microformal"  or "thick" morphisms of (super)manifolds and their quantum counterparts, which can be viewed as Fourier integral operators (FIOs) of certain type. (Classical) thick morphisms that intertwine odd Hamiltonians specifying S-infinity structures on supermanifolds induce as pullbacks L-infinity morphisms for the corresponding odd Poisson brackets. Likewise, quantum thick morphisms commuting with "Batalin-Vilkovisky operators" also yield L-infinity morphisms, but now for the "quantum" brackets generated by the BV operators. I will explain both theorems and show how the relation between them resembles the classical Egorov theorem, which was one of the foundation stones for Hörmander's theory of FIOs.

Import this event to your Outlook calendar
▲ Up to the top