Spring 2020 Talks

Day	Speaker	Title
02/03	Ningchuan	Exotic elements in Picard groups In this talk, I will discuss the subgroup of exotic elements in the K(h)-local Picard groups. We will first show this subgroup is zero when p≫h and then focus on the (h,p)=(1,2) and (2,3) cases.
02/10	Ningchuan	Exotic elements in Picard groups
02/17	Brian	A geometric perspective on the foundations of modern homotopy theory Homotopy theorists have always been interested in studying spaces. However, the meaning of the word ``space’’ has evolved over the years. Whereas one used to say space to mean a topological space, it seems the modern stance is to view a space as an ∞-groupoid. In this expository talk, I would like to connect the modern stance back to geometry. In particular, I will demonstrate how the ∞-category of spaces can be built out of the category of manifolds. As an application, we will use this connection to give a geometric perspective on infinite loop space theory.
02/24	Brian	An introduction to motivic homotopy theory Motivic homotopy is often thought of as the homotopy theory of algebraic varieties. In this expository talk, we’ll see exactly what that means. In particular, we’ll see how the construction of the category of motivic spaces is a direct algebro-geometric analog of that of the category of spaces. More interestingly, we’ll also see how the analogy breaks down.
03/09	Tsutomu	Some applications of tangent categories The cotangent complex formalism is a useful framework for developing obstruction theoretic tools such as Andre-Quillen cohomology. I will present a theorem that identifies the tangent categories of Cat_S, where S is some symmetric monoidal infinity-category. Some more example applications of this formalism will follow.