This is the webpage for my portion of the seminar An invitation to factorization algebras, which I'm co-teaching with Prof. Peter Teichner at UC Berkeley during the spring 2016 semester. You can find his course website here. The seminar meets Tu/Th 2-3:30 in 75 Evans.
In this part of the course, we'll be focusing on the theory of locally constant factorization algebras. From a physical perspective, these arise in the limit that our QFTs become TQFTs, i.e. become independent of any local geometric structure. This setting is far better understood from a mathematical perspective, and admits exciting connections with derived algebra(ic geometry) and deformation theory.
We will see three main results:
1. the classification of homology theories for manifolds;
2. nonabelian Poincaré duality;
3. Poincaré/Koszul duality.
You can see a very slightly extended description of these topics at the beginning of the lecture notes.
lecture notes: This link will be regularly updated. Also, here is a picture of the big diagram attempting to summarize the relationship between relative categories, model categories, quasicategories, and ∞-categories.
Ayala--Francis, Factorization homology of topological manifolds (results 1 and 2)
Ayala--Francis, Poincaré/Koszul duality (result 3)
Lurie, Chapter 1 of Higher topos theory (background on ∞-categories)
Lurie, Moduli problems for ring spectra (background on formal moduli problems and deformation theory)
Ayala--Francis--Tanaka, Local structures on stratified spaces and Factorization homology of stratified spaces (foundations of a stratified version of the theory -- connects to knot theory and intersection co/homology)
Ayala--Francis--Rozenblyum, A stratified homotopy hypothesis and Factorization homology from higher categories (connects to (∞,n)-category theory)