# Mathematics

## Geometricity and Galois actions on fundamental groups

## The stable cohomology of the moduli space of curves with level structures

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

## Stable cohomology of complements of discriminants

## The circle method and the cohomology of moduli spaces of rational curves

## E_2 algebras and homology - 2 of 2

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

## Coincidences between homological densities, predicted by arithmetic - 2 of 2

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

## Representation stability and asymptotic stability of factorization statistics

## 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