# School of Mathematics

## The min-max width of unit volume three-spheres

## Caustics of fronts and the arborealization conjecture

## Four and a half proofs of a product-measure version of the Erdös-Ko-Rado Theorem.

The EKR theorem, which is the cornerstone of extremal combinatorics, characterizes maximal intersecting families of sets. Its setting fixes a ground set of size n, and then studies the size and structure of intersecting families of subsets of fixed size k. A setting which many might consider no less natural, is considering the Boolean lattice of all subsets of {1,...,n} endowed with a product measure, and studying the structure and measure of maximal intersecting families.

## Perverse schobers and semi-orthogonal decompositions

## On the proof of the conservativity conjecture

Abstract: I will review the strategy of the proof of the conservativity conjecture for the classical realisations of Voevodsky motives over a characteristic zero fields. I will also mention some other consequences of this proof such as the nilpotence of endomorphisms acting by zero on cohomology.