# Mathematical Sciences Research Institute

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# Seminar

Thursday Online Seminar: Enriched factorization homology in dimension 1 April 02, 2020 (10:00 AM PDT - 11:30 AM PDT)
Parent Program: MSRI: Online/Virtual
Speaker(s) Aaron Mazel-Gee (California Institute of Technology)
Description No Description
Video

#### Enriched Factorization Homology In Dimension 1

Abstract/Media

To join this or any of the MSRI hosted talks this week please use the following link.

https://msri.zoom.us/s/585445592

Thus far in the factorization homology learning seminar, we have primarily discussed factorization homology of E_n-algebras (informally referred to as "factorization homology alpha"). For E_n-algebras in spaces, this admits a generalization to (∞,n)-categories (informally referred to as "factorization homology beta"). In the case that n=1, this has been extended further to enriched (∞,1)-categories.

In this talk, I will carefully explain both factorization homology beta and enriched factorization homology in dimension 1. I will also discuss its functoriality, leading to the cyclotomic structure on topological Hochschild homology (THH). Along the way, we'll see various familiar combinatorially-defined categories (such as Connes's cyclic category) arising naturally within the context of manifold topology.

This represents various joint works among David Ayala, John Francis, Nick Rozenblyum, and myself.