Video Lectures

Forming Massive Galaxies

December 01, 2015

Pieter van Dokkum

The talk begins in 2005, with the unexpected discovery that massive early-type galaxies were extremely compact at redshifts z~2. It is now thought that the remarkable size growth of these galaxies from z=2 to z=0 is largely due to minor mergers; the...

video lecture

Volume and homology for hyperbolic 3-orbifolds, and the enumeration of arithmetic groups I & II

December 01, 2015

Peter Shalen

A theorem of Borel's asserts that for any positive real number $V$, there are at most finitely many arithmetic lattices in ${\rm PSL}_2({\mathbb C})$ of covolume at most $V$, or equivalently at most finitely many arithmetic hyperbolid $3$-orbifolds...

video lecture

Rigidity of random Toeplitz matrices with an application to depth three circuits

December 01, 2015

Avishay Tal

Joint work with Oded Goldreich. We prove that random $n$-by-$n$ Toeplitz matrices over $GF(2)$ have rigidity $\Omega(n^3/(r^2 \log n))$ for rank $r > \sqrt{n}$, with high probability. This improves, for $r = o(n / \log n \log\log n)$, over the $...

video lecture

Billiards in quadrilaterals, Hurwitz spaces, and real multiplication of Hecke type

November 30, 2015

Alexander Wright

After a brief introduction to the dynamics of the $\mathrm{GL}(2,\mathbb R)$ action on the Hodge bundle (the space of translations surfaces), we will give a construction of six new orbit closures and explain why they are interesting. Joint work with...

video lecture

Lower bounds on the size of semidefinite programming relaxations

November 30, 2015

David Steurer

We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the linear image...

video lecture

Hausdorff dimension of Kleinian group uniformization of Riemann surface and conformal rigidity

November 24, 2015

Yong Hou

For this talk I'll discuss uniformization of Riemann surfaces via Kleinian groups. In particular question of conformability by Hasudorff dimension spectrum. I'll discuss and pose some questions which also in particular will imply a conjecture due to...

video lecture

General systems of linear forms: equidistribution and true complexity

November 24, 2015

Pooya Hatami

Higher-order Fourier analysis is a powerful tool that can be used to analyse the densities of linear systems (such as arithmetic progressions) in subsets of Abelian groups. We are interested in the group $\mathbb{F}_p^n$, for fixed $p$ and large $n$...

video lecture

Fun with finite covers of 3-manifolds: connections between topology, geometry, and arithmetic

November 23, 2015

Nathan Dunfield

Following the revolutionary work of Thurston and Perelman, the topology of 3-manifolds is deeply intertwined with their geometry. In particular, hyperbolic geometry, the non-Euclidean geometry of constant negative curvature, plays a central role. In...

video lecture

Advances on Ramsey numbers

November 23, 2015

Jacob Fox

Ramsey theory refers to a large body of deep results in mathematics whose underlying philosophy is captured succinctly by the statement that "Every very large system contains a large well-organized subsystem." Ramsey numbers capture how very large...

video lecture

Geometric deformations of orthogonal and symplectic Galois representations

November 19, 2015

Jeremy Booher

For a representation of the absolute Galois group of the rationals over a finite field of characteristic $p$, we would like to know if there exists a lift to characteristic zero with nice properties. In particular, we would like it to be geometric...