Video Lectures

Matroids are combinatorial structures that model independence, such as that of edges in a graph and vectors in a linear space. I will introduce the theory of matroids along with their surprising connection to a class of multivariate polynomials that...

One can associate an HDHF (symmetric) wrapped Fukaya category to a Liouville domain by counting higher genus curves, which are required to be branched covers. For the cotangent bundle of an orientable surface with genus at least one Honda, Tian, and...

We propose and study a new arithmetic invariant of non-hyperelliptic genus-4 curves: a canonical “quadratic” point on the Jacobian, defined by the two natural degree-2 maps to projective lines. Building on Xue’s result, that this point is...

The Khovanskii-Teissier inequality provides the fundamental log-concavity property of intersection numbers of divisors of algebraic varieties, extending the Alexandrov-Fenchel inequality of convex geometry. In this talk I will explain, and attempt...

For a complex elliptic curve E and a point p of order n on it, the images of the points pk=kp under the Weierstrass embedding of E into CP2 are collinear if and only if the sum of indices is divisible by n. We prove that for n at least 10 a...

Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat 3-manifolds which we call translation prisms. Using ideas of Furstenberg, and Veech, we connect results about weak mixing properties of flows on...

Several recent groundbreaking results in geometric measure theory, homogeneous dynamics and number theory ultimately rely on a key result of Bourgain known as Bourgain's Projection Theorem (of course, each of these results require many other tools...

I will start by reviewing various Hodge-theoretic invariants of complex singularities. After that, I will discuss how to study such singularities using methods of positive characteristic such as Cartier operators. This is based on joint work with...

This talk will be about two related results, one in complexity theory and one in learning.

On the learning side, we investigate the sample complexity of smooth boosters - These are boosting algorithms that do not place too much weight on any given...