Talk 1: Triangulated surfaces in triangulated categories
Abstract: The symmetries inherent in the structure constants of a Frobenius algebra can be used to associate certain numerical invariants of oriented surfaces. These numbers behave nicely when chopping surfaces into pieces - in technical terms they form a 2-dimensional open topological field theory. In particular, the invariant of a given surface can be computed in terms of a chosen triangulation. In this talk, we explain how certain symmetries in the foundations of homological algebra behave like a Frobenius algebra to the extent that they define invariants of oriented surfaces.
Based on joint work with Mikhail Kapranov. "
" Talk 2: Relative Calabi-Yau structures [Salle Eole, à 14:00]
Abstract: The basic operation of oriented cobordism is to glue two oriented manifolds along a common boundary component to produce a new oriented manifold. In this talk, we discuss a generalization of this procedure to noncommutative geometry: we introduce the concept of a Calabi-Yau structure on a functor of differential graded categories which should be interpreted as an analog of an oriented manifold with boundary. As an application of the resulting theory, we show that topological 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. "
comments