Video Lectures

The second and fourth moments of the Riemann zeta function have been known for about a century, but the sixth moment remains elusive.  

The sixth moment of zeta can be thought of as the second moment of a GL_3 Eisenstein series, and it is natural to...

Superradiant instabilities may create clouds of ultralight bosons around rotating black holes, forming so-called "gravitational atoms". In this talk, I will review a series of papers that study the effects of a binary companion’s presence. The...

In the third talk, I will concentrate on inequalities for linear extensionsof finite posets.  I will start with several inequalities which do have a combinatorial proof.  I will then turn to Stanley's inequality and outline the proof why its defect...

The Arithmetic Quantum Unique Ergodicity (AQUE) conjecture predicts that the L2 mass of Hecke-Maass cusp forms on an arithmetic hyperbolic manifold becomes equidistributed as the Laplace eigenvalue grows. If the underlying manifold is non-compact...

Fourier Quasicrystals (FQ) are defined as crystalline measures

μ=∑λ∈Λaλδλ,μ̂ =∑s∈Sbsδs, so that not only μ (and hence μ̂ ) are tempered distributions, but also |μ|:=∑λ∈Λ|aλ|δλand|μ̂ |:=∑s∈S|bs|δs,

are tempered.

One-dimensional FQs with positive...

In the second talk, I will concentrate on polynomial inequalities and whether the defect (the difference of two sides) has a combinatorial interpretation.  For example, does the inequality  x2+y2≥2xy

  have a combinatorial proof and what does that...

In the previous talk, we defined Subgroup Tests and the interactive proof system induced by them. In addition, we showed that if the Aldous--Lyons conjecture was true, then this interactive proof system contains only decidable languages. In this...

By Deligne's Hodge theory, the integral cohomology groups H^n(X^h, Z) of the C-analytification of a separated scheme X of finite type over C are provided with a mixed Hodge structure, functorial in X. Given a non-Archimedean field K isomorphic to...