Fall 2017

Luis Scoccola, Introduction to Homotopy Type Theory and Synthetic Homotopy Theory
(Tuesday Sep 19, 2017)

The role of types in Type Theory is very similar to the role of sets in Set Theory. One key difference is that equality in HoTT behaves more like homotopy in topology, rather than equality in set theory. This observation motivates the use of HoTT as a language to study homotopy theory. Time permitting, we will illustrate the encode-decode technique -- used to characterize the groupoid-like structure of certain types -- in the case of localizations.

James Richardson, Introduction to Derivators
(Tuesday Oct 3, 2017)

Derivators are a framework for studying homotopy theory. In this talk we will give an informal introduction to derivators, discuss some examples, and discuss the relationship between derivators and other models of homotopy theory.

Dinesh Valluri, Moduli Problems and Stacks
(Tuesday Oct 17, 2017)

In this talk we will discuss what moduli problems are and why they are important in algebraic geometry, with some examples. We will introduce the idea of a stack and give examples to illustrate why it is a natural notion. If time permits we will discuss how one can compute the dimension of certain moduli spaces using Riemann-Roch.

Jasmin Omanovic, Open questions in Quadratic forms
(Tuesday Oct 31, 2017 -- Cancelled)

In this talk I will present several classical results concerning the relationship between quadratic forms, central simple algebras, Milnor K-theory, Galois cohomology and Severi-Brauer varieties. The central theme of this talk will be to ask the questions which have both then and now resisted all efforts toward a solution.

Alexander Rolle, Abelianization in Algebraic Topology
(Tuesday Nov 14, 2017)

The talk will begin with an introduction to the simplicial approach to singular homology, as a paradigm of "abelianization". Then, there will be some discussion of the generalization of this idea to simplicial presheaves, and, time permitting, further generalizations to motivic cohomology.