School of Mathematics
The (Counter-Intuitive) Geometry of Cut and Flow Polytopes
Limit Theorems in Pseudorandomness
Properties of Random Group Elements
Mechanism Design With Set-Theoretic Beliefs
In settings of incomplete information, we put forward (1) a very conservative ---indeed, purely set-theoretic--- model of the beliefs (including totally wrong ones) that each player may have about the payoff types of his opponents, and (2) a new and robust solution concept, based on mutual belief of rationality, capable of leveraging such conservative beliefs.
On Singularities With Rational Homology Disk Smoothings
Multiplicities and the Equivariant Index
Shadowing and Diffusion in Hamiltonian Systems
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