Members Seminar

In this talk, I will discuss the behavior of hard-core lattice particle systems at high fugacities. I will first present a collection of models in which the high fugacity phase can be understood by expanding in powers of the inverse of the fugacity...

We introduce the notion of a "crystallographic sphere packing," which generalizes the classical Apollonian circle packing. Tools from arithmetic groups, hyperbolic geometry, and dynamics are used to show that, on one hand, there is an infinite zoo...

Locally symmetric spaces are a class of Riemannian manifolds which play a special role in number theory. In this talk, I will introduce these spaces through example, and show some of their unusual properties from the point of view of both analysis...

Four years ago, Cachazo, He and Yuan found a system of algebraic equations, now named the "scattering equations", that effectively encoded the kinematics of massless particles in such a way that the scattering amplitudes, the quantities of physical...

Combinatorial geometry is a field that studies combinatorial problems that involve some simple geometric objects/notions, such as: lines, points, distances, collinearity. While such problems are often easy to state, some of them are very difficult...

The sum-of-squares (SOS) hierarchy (due to Shor'85, Parrilo'00, and Lasserre'00) is a widely-studied meta-algorithm for (non-convex) polynomial optimization that has its roots in Hilbert's 17th problem about non-negative polynomials.

SOS plays an...

Over the past two decades, information theory has reemerged within computational complexity theory as a mathematical tool for obtaining unconditional lower bounds in a number of models, including streaming algorithms, data structures, and...

Berkovich geometry is an enhancement of classical rigid analytic geometry. Mirror symmetry is a conjectural duality between Calabi-Yau manifolds. I will explain (1) what is mirror symmetry, (2) what are Berkovich spaces, (3) how Berkovich spaces...

The Hofer-Zehnder capacity of a symplectic manifold is one of the early symplectic invariants: it is a non-negative real number, possibly infinite. Finiteness of this capacity has strong consequences for Hamiltonian dynamics, and it is an old...