Algebra/Topology seminar

Speaker: Rhiannon Savage

Title: Representability of Derived Bornological Stacks

Abstract: Derived algebraic geometry can be considered as homotopical geometry relative to the category of simplicial commutative rings. Similarly, new foundations for derived analytic and smooth geometry were proposed last year by Ben-Bassat, Kelly, and Kremnizer as homotopical geometries relative to categories of simplicial commutative complete bornological rings. In this talk I will introduce this framework and discuss a version of the Artin-Lurie representability theorem which holds for derived stacks in these contexts. I will also briefly discuss ongoing work showing representability of moduli stacks of solutions to PDEs. No knowledge of analytic or smooth geometry is assumed.