# School of Mathematics

## Symplectic and Spectral Theory of Integrable Systems

## Multiplicities and the Equivariant Index

## On Singularities With Rational Homology Disk Smoothings

## Problems of Ideal Incompressible Fluids

## Shadowing and Diffusion in Hamiltonian Systems

## Tight Lower Bounds for 2-query LCCs Over Finite fields

A locally correctable code (LCC) is an error correcting code mapping d symbols to n symbols, such that for every codeword c and every received word r that is \delta-close to c, we can recover any coordinate of c (with high probability) by only making a few queries to r. LCCs are a stronger form of Locally Decodable Codes (LDCs) which have received a lot of attention recently due to their many applications and surprising constructions.

## Nonnegative k-Sums, Fractional Covers, and Probability of Small Deviations

## First Steps in Symplectic Dynamics

The modern theory of dynamical systems, as well as symplectic geometry, have their origin with Poincare as one field with integrated Ideas. Since then these fields developed quite independently. Given the progress in these fields one can make a good argument why the time is ripe to bring them closer together around the core area of Hamiltonian dynamics