Video Lectures

Lévy matrices are symmetric random matrices whose entries are in the domain of attraction of an \alpha stable law. For \alpha 1, it had been predicted that these matrices exhibit an Anderson transition, also called a mobility edge, a point in the...

We present recent developments in symplectic geometry and explain how they motivated new results in the study of cluster algebras. First, we introduce a geometric problem: the study of Lagrangian surfaces in the standard symplectic 4-ball bounding...

Super star clusters with masses > 1e6 Msun are thought to be progenitors of globular clusters (GCs). Their births however are seldomly seen in the local Universe. Given radiation and kinetic feedbacks that regulate star formation, contribution to...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

The Study of Pre-modern Hebrew Philosophical and Scientific Terminology as a new Chapter in the Intellectual History of Europe and the Islamicate World: PESHAT in Context. 

Speakers: Giuseppe Veltri (University of Hamburg), Reimund Leicht (Hebrew...

Given any non-negative function \f:ℤ→ℝ, it follows from basic ergodic ideas that either 100% of real numbers α have infinitely many rational approximations a/q with a,q coprime and |α−a/q|

I'll describe a recent resolution of this conjecture, which recasts the problem in combinatorial language, and then uses a general 'structure vs randomness' principle combined with an iterative argument to solve this combinatorial problem.

The celebrated product theorem says if A is a generating subset of a finite simple group of Lie type G, then |AAA| \gg \min \{ |A|^{1+c}, |G| \}. In this talk, I will show that a similar phenomenon appears in the continuous setting: If A is a subset...

The talk will consists of a long historical introduction to  the topic of deviation of ergodic averages for locally Hamiltonian flows on compact surafces  as well as some current results obtained in collaboration with Corinna Ulcigrai  and Minsung...

The theory of graph quasirandomness studies sequences of graphs that "look like" samples of the Erdős--Rényi random graph. The upshot of the theory is that several ways of comparing a sequence with the random graph turn out to be equivalent. For...

Given several real numbers α1,...,αk, how well can you simultaneously approximate all of them by rationals which each have the same square number as a denominator? Schmidt gave a clever iterative argument which showed that this can be done...