# Mathematics

## Quillen's Devissage in Geometry

In this talk we discuss a new perspective on Quillen's devissage theorem. Originally, Quillen proved devissage for algebraic -theory of abelian categories. The theorem showed that given a full abelian subcategory of an abelian category , if every object of has a finite filtration with quotients lying in . This allows us, for example, to relate the -theory of torsion -modules to the -theories of -modules for all . Generalizations of this theorem to more general contexts for -theory, such as Walhdausen categories, have been notoriously difficult; although some such theorems exist they are generally much more complicated to state and prove than Quillen's original. In this talk we show how to translate Quillen's algebraic approach to a geometric context. This translation allows us to construct a devissage theorem in geometry, and prove it using Quillen's original insights.

## A^1 enumerative geometry: counts of rational curves in P^2 - 2 of 2

This is the second lecture in a two part series: part 1

## Conjectures, heuristics, and theorems in arithmetic statistics - 1 of 2

## E_2 algebras and homology - 1 of 2

This is the first lecture in a two part series: part 2

## The Grothendieck ring of varieties, and stabilization in the algebro-geometric setting - part 1of 2

In the first lecture of this minicourse, Ravi Vakil will introduce the ring, and describe how it can be used to prove or suggest such stabilization in several settings.

This is the first lecture in a two part series: part 2

In the second lecture of the minicourse, Aaron Landesman will use these ideas to describe a stability of the space of low degree covers (up to degree 5) of the projective line (joint work with Vakil and Wood). The results are cognate to Bhargava’s number field counts, the philosophy of Ellenberg-Venkatesh-Westerland, and Anand Patel’s fever dream.

## Point counting and topology - 1 of 2

This is the first lecture in a two part series: part 2

## 2019 Workshop on Mathematical Sciences and Clean Energy Applications

This gallery contains photos from the 2019 Workshop on Mathematical Sciences and Clean Energy Applications. See the event webpage for more information

## A^1 enumerative geometry: counts of rational curves in P^2 - 1 of 2

This is the first lecture in a two part series: part 2

## A1-homotopy of the general linear group and a conjecture of Suslin

## Geometric Aspects of Arithmetic Statistics - 2 of 2

This is the second of a two part series: part 1