# Recently Added

## Problems of Ideal Incompressible Fluids

## 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.

## 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

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

## On Real Zeros of Holomorphic Hecke Cusp Forms and Sieving Short Intervals

A. Ghosh and P. Sarnak have recently initiated the study of so-called real zeros of holomorphic Hecke cusp forms, that is zeros on certain geodesic segments on which the cusp form (or a multiple of it) takes real values. In the talk I'll first introduce the problem and outline their argument that many such zeros exist if many short intervals contain numbers whose all prime factors belong to a certain subset of primes. Then I'll speak about new results on this sieving problem which lead to improved lower bounds for the number of real zeros.

## Limit Theories and Higher Order Fourier Analysis

## A Little Advice Can Be Very Helpful

## Stochastic Twist Maps and Symplectic Diffusions

## C^0 Limits of Hamiltonian Paths and Spectral Invariants

After reviewing spectral invariants, I will write down an estimate, which under certain assumptions, relates the spectral invariants of a Hamiltonian to the C^{0}-distance of its flow from the identity. I will also show that, unlike the Hofer norm, the spectral norm is C^{0}-continuous on surfaces. Time permitting, I will present an application to the study of area preserving disk maps.