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Tuesday, February 19, 2019

**Abstract:** Factorization algebras are a mathematical tool used to encode the data of the observables of a field theory. There are various notions of factorization algebra: one can define a factorization algebra on the open subsets of some fixed manifold; or alternatively, one can define a factorization algebra on the site of all manifolds of a given dimension with specified geometric structure. In this talk I will outline a comparison between two such notions: G-equivariant factorization algebras on a fixed model space M and factorization algebras on the site of all manifolds quipped with a (G, M)-structure (given by an atlas of charts in M and transition maps in G). I will introduce the definitions of these two concepts and then sketch the proof of their equivalence as (\infy,1)-categories.