Junior Geometry and QFT Seminar

This is the first part of the series talk on 'Topological quantum field theory (TQFT) arising from derived algebraic geometry (DAG)'. The goal of this talk is to introduce the construction of a TQFT from an algebraic variety. This may seem unexpected because TQFT resides in the realm of topology, while our input data is an object of algebraic geometry. However, derived algebraic geometry blurs the boundary between those two domains. A striking manifestation of this slogan is that we can associate an algebro-geometric space to any topological space. Using this interaction, Ben-Zvi, Nadler, and Francis constructed a TQFT that gives a far-reaching generalization of the finite TQFT introduced by Dijkgraaf and Witten. The goal of this talk has two main aims: a) to motivate this construction by reviewing some aspects of finite gauge theory, b) to introduce the formalism of DAG.