David Ayala

Title: Singular field theories

Abstract:  This talk will examine a bordism category consisting of
manifolds with prescribed singularities.  A classification of functors
from such bordism categories will be presented.  This classification
draws a correspondence between imposing certain relations on the
(algebraic) data of a field theory and extending the field theory to
singular manifolds of a certain type.  Applications to Gromov-Witten
theory and to universal characteristic classes will be discussed.