## Contact non-squeezing in $\mathbb R^{2n} \times S^1$ by other means

## Sheaves and contact non-squeezing in $\mathbb R^{2n} \times S^1$

## Algebraic proofs of degenerations of Hodge-de Rham complexes

In the first half of the talk I shall present a new algebraic proof of a result of Deligne-Illusie about the degeneration of the Hodge-de Rham spectral sequence. The idea is to reduce the main technical point of their proof to a question about the formality of a derived intersection in an Azumaya space.

## Soliton resolution for energy critical wave and wave map equations

## Mirror symmetry for moduli of flat bundles and non-abelian Hodge theory

## Noncommutative probability for computer scientists

## In pursuit of obfuscation

## Two rigid algebras and a heat kernel

## Basic loci of Shimura varieties

In mod-$p$ reductions of modular curves, there is a finite set of supersingular points and its open complement corresponding to ordinary elliptic curves. In the study of mod-$p$ reductions of more general Shimura varieties, there is a "Newton stratification" decomposing the reduction into finitely many locally closed subsets, of which exactly one is closed. This closed set is called the basic locus; it recovers the supersingular locus in the classical case of modular curves.