Video Lectures

We consider the space of configurations of n points in the three-sphere S3, some of which may coincide and some of which may not, up to the free and transitive action of SU(2) on S3. We prove that the cohomology ring with rational coefficients is...

Every braid can be thought of as a homeomorphism of a punctured disc. Morally, the more complicated a braid is, the more dynamics is contained in the corresponding homeomorphism, which one can quantify using topological entropy. In particular, one...

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...

On-shell methods have found a new application to local observables such as asymptotic radiation fields and gravitational waveforms. While these observables are invariant under small gauge transformations, they are known to depend on a choice of...

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...