Andy Manion - Higher representations and cornered Heegaard Floer homology

June 4, 12 pm ET: Andy Manion (University of Southern California), Higher representations and cornered Heegaard Floer homology

Abstract: I will survey recent work with Raphael Rouquier from the perspective of partially wrapped Fukaya categories of symmetric products of surfaces and related algebras known as bordered strands algebras. I will try to motivate how higher representation theory enters the story when studying how to recover Fukaya categories of symmetric powers of a glued-together surface from the pieces as in cornered Heegaard Floer homology, and to show how formulas describing such gluings are related to a new type of tensor product operation in higher representation theory.

Questions

00:14:11 Mohammed Abouzaid: Can I make sure that I understand something: this is a disjoint union over k with no interaction between the different factors

00:48:07 Mohammed Abouzaid: I would have naively expected i+j=k. Is there an easy way to see why that's not the case