Video Lectures

According to the conjecture of Bondal, the derived category of coherent sheaves on any smooth projective variety can be embedded as a semiorthogonal component into the derived category of a Fano variety of higher dimension. I will explain how this...

We consider elliptic curves whose coefficients are degree 2 polynomials in a variable $t$. We prove that for infinitely many values of $t$ the resulting elliptic curve has rank at least 1. All such curves together form an algebraic surface which is...

The sensitivity conjecture is a major outstanding foundational problems about boolean functions is the sensitivity conjecture. In one of its many forms, it asserts that the degree of a boolean function (i.e. the minimum degree of a real polynomial...

Crow examines the displaced and wandering existences of Jacques-Louis David and Théodore Géricault, both in geographical and psychological exile, during which each was forced to reexamine and reconfigure the fundamentals of his artistic life. The...

The André-Oort conjecture says that any subvariety of a Shimura variety with a Zariski dense set of CM points must itself be a Shimura subvariety. In recent years, this has been the subject of much work. We explain how this conjecture for the moduli...

Michele Beck has received acclaim for her work in video and performance. In her videos she often films herself wearing costumes of her own making, concealing her entire body, head and face. In My Erotic Body, a work that could broadly be...

Let $S$ and $T$ be two dense subsets of $G^n$, where $G$ is the special linear group $\mathrm{SL}(2,q)$ for a prime power $q$. If you sample uniformly a tuple $(s_1,\ldots,s_n)$ from $S$ and a tuple $(t_1,\ldots,t_n)$ from $T$ then their interleaved...

In this talk I'll discuss a lattice point count for a thin semigroup inside $\mathrm{SL}_2(\mathbb Z)$. It is important for applications I'll describe that one can perform this count uniformly throughout congruence classes. The approach to counting...

One of the most effective methods for solving boundary value problems for basic elliptic equations of mathematical physics in a given domain is the method of layer potentials. Its essence is to reduce the entire problem to an integral equation on...