Previous Conferences & Workshops

We study the complexity of constructing a hitting set for the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. Specifically, we...

It is well known that an irreducible representation of a group $G$ over a field $k$ admits a universal deformation to a representation over a complete Noetherian local ring, provided that it is absolutely irreducible, i.e. remains irreducible after...

Knot contact homology is a knot invariant derived from counting holomorphic curves with boundary on the Legendrian conormal to a knot. I will discuss some new developments around the subject, including an enhancement that completely determines the...

Symplectic Geometry and its dynamics originated from classical mechanics as the geometry of physical phase space, in particular from celestial mechanics, and one of the most driving questions is up to today that of stability for such systems. One of...

The current successes of deep neural networks have largely come on classification problems, based on datasets containing hundreds of examples from each category. Humans can easily learn new words or classes of visual objects from very few examples...

It is classically understood how to learn the parameters of a Gaussian even in high dimensions from independent samples. However, estimators like the sample mean are very fragile to noise. In particular, a single corrupted sample can arbitrarily...

Constructive vs Pure Existence proofs have been a topic of intense debate in foundations of mathematics. Constructive proofs are nice as they demonstrate the existence of a mathematical object by describing an algorithm for building it. In computer...

The classical affine cubic surface of Markoff has a well-known interpretation as a moduli space for local systems on the once-punctured torus. We show that the analogous moduli spaces for general topological surfaces form a rich family of log Calabi...

For integer parameters $n \geq 3$, $a \geq 1$, and $k \geq 0$ the Markoff-Hurwitz equation is the diophantine equation \[ x_1^2 + x_2^2 + \cdots + x_n^2 = ax_1x_2 \cdots x_n + k.\] In this talk, we establish an asymptotic count for the number of...

We report on some recent work with Peter Sarnak. For integers $k$, we consider the affine cubic surfaces $V_k$ given by $M(x) = x_1^2 + x_2 + x_3^2 − x_1 x_2 x_3 = k$. Then for almost all $k$, the Hasse Principle holds, namely that $V_k(Z)$ is non...