Classification of (semisimple) TQFTs

For zoom details contact Peter Teichner (teichner@mpim-bonn.mpg.de) or David Reutter.

 If you ask a mathematician for a classification of (fully extended, framed) TQFTs, she will probably tell you that they are classified by fully-dualizable objects of the target n-category, and in particular the classification depends on your choice of target n-category. If you ask a physicist, on the other hand, she will tell you that "(T)QFT" is a primitive notion, and that the classification question has a well-defined answer. These two perspectives combine into the following challenge: define, construct, and analyze the "universal target category" in which all TQFTs take values. In this talk, I will describe the solution to this challenge in the case of semisimple TQFTs. This is joint work in progress with David Reutter.