Microformal geometry and homotopy algebras
Speaker: Ted Voronov, The University of Manchester
Abstract: I will introduce the construction of microformal (also known as "thick") morphisms of supermanifolds and their main properties. Thick morphisms include ordinary smooth maps as a particular case and, the same as for ordinary maps, they induce pullbacks of functions. The crucial difference is that in general these pullbacks are non-linear; they are defined by a perturbative procedure and have a form of formal non-linear differential operators. Non-linear pullbacks by thick morphisms give L-infinity morphisms for homotopy Poisson structures, for example, arising from L-infinity algebroids. (The non-linearity of pullbacks is what is responsible for higher homotopies.) There exist two parallel versions of thick morphisms, "bosonic" and "fermionic". The bosonic version possesses a "quantum counterpart" given by certain type Fourier integral operators. "Quantum microformal morphisms" induce L-infinity morphisms for "quantum BV-algebras". Time permitting, I may also speak about some of the most recent developments such as the extension of the tangent functor to thick morphisms.
Room Reservation Information
Room Number: 320 Whitmore
Time: 2:30pm - 3:30pm