Algebra/Topology Seminar

Speaker: Germán Stefanich (Max Planck Institute for Mathematics)
Title: Higher algebraic geometry
Abstract:
The goal of this talk will be to explain joint work with Scholze where we study a version of algebraic geometry which is built, not out of spectra of commutative rings, but out of spectra of symmetric monoidal higher categories. The resulting world of geometry contains the classical category of algebraic varieties, but also provides a home to new and interesting objects which cannot be studied with more classical means. In particular, I hope to explain the role that some of these objects play in ongoing work with Ben-Zvi and Nadler on various Langlands duality statements in the context of three dimensional topological field theory.