Derived stacks of algebraic structures

Speaker: Sinan Yalin

Title: Derived stacks of algebraic structures

Abstract: I will start by explaining how props parametrise various bialgebra structures and form a model category. Cofibrant resolutions of props define algebraic structures up to homotopy, which occur in a prominent way
in various topics of geometry and topology. I will explain that such a definition does not depend, up to homotopy, on the choice of a resolution. A meaningful idea to understand the behavior of such structures is to study
them as a moduli problem. For this, I will define the notion of simplicial moduli space of algebraic structures, and show how these moduli spaces fit in the setting of Toen-Vezzosi's derived algebraic geometry.