School of Mathematics

One of the central problems of coding theory is to determine the trade-off between the amount of information a code can carry (captured by its rate) and its robustness to resist message corruption (captured by its distance). One of the main methods...

Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas.  In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is...

Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas.  In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is...

I will discuss the difficult problem of proving reasonable bounds in the multidimensional generalization of Szemer\’edi’s theorem and describe a proof of such bounds for sets lacking nontrivial configurations of the form $(x,y), (x,y+z), (x,y+2z),...

We will discuss some old and new results concerning the long-time behavior of solutions to the two-dimensional incompressible Euler equations.  Specifically, we discuss whether steady states can be isolated, wandering for solutions starting nearby...

One of the central problems of coding theory is to determine the trade-off between the amount of information a code can carry (captured by its rate) and its robustness to resist message corruption (captured by its distance). On the existential side...

Understanding the behavior of multi-player (multi-prover) games under parallel repetition is an important problem in theoretical computer science.

In a k-player game G, a referee chooses questions (x1,...,xk) from a (publicly known)...

In this talk, I want to show that in the planar circular restricted three body problem there are infinitely many symmetric consecutive collision orbits for all energies below the first critical energy value.  By using the Levi-Civita regularization...

Liouville field theory was introduced by Polyakov in the eighties in the context of string theory. Liouville theory appeared there under the form of a 2D Feynman path integral, which can be thought of as a measure (or expectation value) over the...

We discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estimates for these metrics conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the...