Video Lectures

We provide a simple proof of the Rota--Heron--Welsh conjecture for matroids realizable as c-arrangements in the sense of Goresky--MacPherson: we prove that the coefficients of the characteristic polynomial of the associated matroids form log-concave...

An important theme in homogenous dynamics is that two parameter diagonalizable actions have much more rigidity than one parameter actions. One manifestation of this rigidity is rigidity of joinings of such actions. Joinings are an important concept...

Given a $k$-edge-connected graph $G = (V,E)$, a spanning tree $T$ is $\alpha$-thin w.r.t. $G$, if for any $S \subset V$, $|T(S,V - S)| \leq \alpha.|E(S,V - S)|$. The thin tree conjecture asserts that for a sufficiently large $k$ (independent of size...

In my talk I will report on recent work with Hansjörg Geiges about a strong connection between the topology of a contact manifold and the existence of contractible periodic Reeb orbits. Namely, if the contact manifold appears as non-trivial contact...

Honoring the 2014 SSRC’s Albert O. Hirschman Prize Recipients Abhijit Banerjee and Esther Duflo Co-Directors, Abdul Latif Jameel Poverty Action Lab Massachusetts Institute of Technology This program features a talk by Esther Duflo, as well as a...

Let $X$ be a smooth canonically polarised surface defined over an algebraically closed field of characteristic 2. In this talk I will present some results about the geometry of $X$ in the case when the automorphism scheme $\mathrm{Aut}(X)$ of $X$...

KSBA (Kollár-Shepherd-Barron-Alexeev) stable pairs are higher dimensional generalizations of (weighted) stable pointed curves. I will present a joint work in progress with Sándor Kovács on proving the projectivity of this moduli space, by showing...

We compare methods of computing inverses of matrices over division rings. The most direct way is via Cohn's theory of full matrices, which was improved by Malcolmson, Schofield, and Westreich. But it is simpler to work with finite dimensional...

A classical problem in the theory of automorphic forms is to count the number of Laplace eigenfunctions on the quotient of the upper half plane by a lattice $L$. For $L$ a congruence subgroup in $\mathrm{SL}(2,\mathbb Z)$ the Weyl law was proven by...