Seminar talk, 4 January 2017

Speaker: Theodore Voronov

Title: Microformal geometry and its applications

Abstract:
The talk will discuss a new notion of microformal" (or "thick") morphisms of smooth (super)manifolds that generalizes ordinary smooth maps. These new morphisms act on smooth maps via pullback that however is a nonlinear transformation. (More precisely, a formal nonlinear differential operator). There appears a formal category, which is a "thickening" of the usual category of (super)manifolds. The construction appeared in relation to homotopic analogs of Poisson structures, for which it gives $L_{\infty }$-morphisms. Another application is an "adjoint operator" for a nonlinear map of vector bundles. One can define also "quantum microformal morphisms", for which the above is the classical limit.

References:
arXiv:1409.6475, arXiv:1411.6720, arXiv:1506.02417, arXiv:1512.04163