Algebra/Topology seminar

Speaker: Tobias Dyckerhoff

Title: Relative Calabi-Yau structures

Abstract: The basic operation of oriented cobordism is to glue twooriented manifolds along a common boundary component to produce a neworiented manifold. In this talk, we discuss a generalization of thisprocedure to noncommutative geometry: we introduce the concept of aCalabi-Yau structure on a functor of differential graded categorieswhich should be interpreted as an analog of an oriented manifold withboundary. As an application of the resulting theory, we show thattopological Fukaya categories of surfaces give rise to a 2D TFT with values in Calabi-Yau cospans of differential graded categories.

Based on joint work in progress with Chris Brav.