Equivariant Factorization Algebras: An Infinity-Operadic Approach

Factorization algebras are a mathematical tool for modeling the observables of field theories. In this dissertation, we consider two particular types of factorization algebras: G-equivariant factorization algebras on a model space M, where G is a group acting on M; and factorization algebras on a site of manifolds which locally look like M and with geometric structure encoded by the G-action. Our main result is that the categories of these factorization algebras are equivalent. To show this, we formulate an alternative, categorical description of the locality (or descent) condition that factorization algebras satisfy, and show that this agrees with the original, more geometric descent condition. We then generalize the definition of factorization algebras to the infinity-operadic setting, and utilize higher algebraic techniques to prove the comparison result. One of the motivations for this new infinity-operadic perspective is the ability to use these general results in future work involving parameterized families of factorization algebras.