Seminars in geometry/topology
Spring 2017 - Upcoming Talks
February 13, 15:00 - 16:00, room 734, Sentralbygg 2
Morten Brun (University of Bergen): Filtered coverings
Abstract: First I will introduce the concept of a filtered covering of a metric space. The defining properties of a filtered covering imply that its nerve is a filtered simplicial complex which is log-interleaved with the filtered Cech complex obtained from coverings by balls of growing size. This is similar to the Vietoris Rips complex being log-interleaved with the Cech complex. Next, given a finite metric space, I will present a specific filtered covering, the cell-dividing covering. The advantage of the cell-dividing covering is that its nerve is quite small, and hence it is practical to compute its persistent homology. Moreover, it is constructed top-down, so that if we disregard fine scale structure of the metric space, then we obtain a very small filtered simplicial complex. In the end of the talk I will present some computations and compare different ways of computing persistent homology.
Spring 2017 - Previous Talks
Januar 9, 14:15 - 15:15, room 656, Sentralbygg 2
Claudia Scheimbauer (MPIM Bonn/University of Oxford): Algebraic structures in topological field theories
Abstract: Atiyah and Segal's axiomatic approach to topological and conformal quantum field theories provided a beautiful link between the geometry of "spacetimes" (cobordisms) and algebraic structures. Combining this with the physical notion of "locality" led to the introduction of the language of higher categories into the field. I will give an introduction to the topic and report on my own work on these "extended" topological field theories – the higher category of cobordisms and a family of examples of extended topological field theories using factorization algebras. Furthermore, I will explain a relative ("twisted") version of field theories and some examples. This is joint work with Calaque, Gwilliam, and Johnson-Freyd.