Video Lectures

More than 120 years ago, Minkowski published a seminal paper that laid the foundation for the field of convex geometry (as well as several other areas of mathematics). Despite numerous advances in the intervening years, there are fundamental...

We will explore certain C0-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is reflected in the group of contact homeomorphisms. We...

Positive selector processes are natural stochastic processes driven by sparse Bernoulli random variables. They play an important role in the study of suprema of general stochastic processes, and in particular, Talagrand posed the selector process...

We will outline the proof of an intersection result between embedded Lagrangian tori and certain 1 parameter families of product Lagrangian tori in the 4 dimensional symplectic cylinder. The theorem can be applied to give new computations of the...

Algebraic statistics employs techniques in algebraic geometry, commutative algebra and combinatorics, to address problems in statistics and its applications. The philosophy of algebraic statistics is that statistical models are algebraic varieties...

The theory of stable polynomials features a key notion called proper position, which generalizes interlacing of real roots to higher dimensions. I will show how a Lorentzian analog of proper position connects the structure of spaces of Lorentzian...

One way to define a matroid is via its base polytope.  From this point of view, some matroid invariants easily have geometric interpretations: e.g., the number of bases is the number of vertices of the polytope.  It turns out that most interesting...

We will present recent applications of enumerative algebra to the study of stationary states in physics. Our point of departure are classical Newtonian differential equations with nonlinear potential. It turns out that the study of their stationary...

The Bergelson conjecture from 1996 asserts that the multilinear polynomial ergodic averages with commuting transformations converge pointwise almost everywhere in any measure-preserving system. This problem was recently solved affirmatively for...

We show that skein valued counts of open holomorphic curves in a symplectic Calabi-Yau 3-fold with Maslov zero Lagrangian boundary condition are invariant under deformations and discuss applications (Ooguri-Vafa conjecture and simple recursion...