Abstract: Functional analytic objects such as topological vector spaces and rings have classically not interact well with homological algebra, stemming from the foundational issue that categories of topological vector spaces are seldom abelian. This has prevented the use of categorical and homotopy-theoretic methods in the study of topological algebras, which constitute the fundamental objects of derived analytic geometry and noncommutative geometry. In this talk, I will present an approach to functional analysis that replaces topological structures with bornologies, ultimately leading to categories that are ideal for the interaction between homotopy theory and analysis. As applications of this framework, I will discuss my ongoing work on derived analytic geometry and p-adic noncommutative geometry.

Meeting id: 948 0044 7244
Passcode: 597063