Infinite-Dimensional Algebra Seminar: Dan Freed (Harvard)

Building 2, Room 135

Speaker: Dan Freed (Harvard University)Where: In-Person at MIT Room 2-135 and onZoom https://mit.zoom.us/j/94469771032?pwd=d3JaSVhVV0xDOGpkUDdveXdOYmNXQT09Title: Finiteness and fusion categoriesAbstract: Fusion categories satisfy stringent finiteness conditions: they are finite semisimple, abelian, rigid, etc. General finiteness conditions occur in higher category theory in the form of dualizability in symmetric monoidal categories. Together with Constantin Teleman, we apply topological quantum field theory--in particular, boundary theories therein--to characterize fusion categories among all tensor categories: fusion categories are tensor categories that are (1) dualizable and (2) the regular module category is also dualizable. The talk will include an exposition of relevant parts of topological field theory.