# Video Lectures

Given a path-connected topological space X, a differential graded (DG) local system (or derived local system) is a module over the DGA of chains on the based loop space of X. I will explain how to define in the symplectically aspherical case...

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...