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.

__references__

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)

__further reading__

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)