Video Lectures

Goldston & Montgomery and Montgomery & Soundararajan have established formulae for the variance of sums of the von Magoldt function over short intervals (i.e. for the variance of the number of primes in these intervals) assuming, respectively, the...

The main object of study of this talk are matrices whose entries are linear forms in a set of formal variables (over some field). The main problem is determining if a given such matrix is invertible or singular (over the appropriate field of...

We show that the bipartite perfect matching problem is in $\textrm{quasi-}\textsf{NC}^2$. That is, it has uniform circuits of quasi-polynomial size and $O(\log^2 n)$ depth. Previously, only an exponential upper bound was known on the size of such...

Looking back through the history of music composition, there is no question that women have been extremely under-represented. In the last few decades that has started to change, and change quickly. Not only are there more and more women writing...

This is joint work with Zhiwei Yun. We prove a generalization of Gross-Zagier formula in the function field setting. Our formula relates self-intersection of certain cycles on the moduli of Shtukas for $\mathrm{GL}(2)$ to higher derivatives of L...

I will describe a formalism for (Lagrangian) Floer theory wherein the output is not a deformation of the cohomology ring, but of the Pontryagin algebra of based loops, or of the analogous algebra of based discs (with boundary on the Lagrangian). I...

In this public lecture, Michael Pettis will explore China’s tumultuous stock market and its impact on the global economy. A Wall Street veteran at Bear Stearns and Credit Suisse First Boston, Pettis has the unique distinction of having been right...

This talk will discuss the question: To what extent are the fundamental groups of compact 3-manifolds determined (amongst the fundamental groups of compact 3-manifolds) by their finite quotients. We will discuss work that provides a positive answer...

We will continue Monday's talk on constant-round interactive proofs, going into more details of the full construction and its proof. We will also briefly recap Monday's talk so that it will be beneficial to those who cannot attend on Monday.

The problem of comparing the shapes of different surfaces turns up in different guises in numerous fields. I will discuss a way to put a metric on the space of smooth Riemannian 2-spheres (i.e. shapes) that allows for comparing their geometric...