Analysis Seminar

In this talk, we will recall the strong openness property of multiplier ideal sheaves (conjectured by Demailly and proved by Guan-Zhou), and then present some recent related progress including some joint work with Professor Xiangyu Zhou.

In this talk, we will recall the strong openness property of multiplier ideal sheaves (conjectured by Demailly and proved by Guan-Zhou), and then present some recent related progress including some joint work with Professor Xiangyu Zhou.

The classical Carleson operator, which is intimately related to the Fourier transform, was an oscillatory singular integral operator with a linear phase. Motivated by a question of Eli Stein, recent consideration of Carleson operators has focused on...

We will show that the appropriately-defined vertical perimeter of a measurable subset of the Heisenberg group is at most a constant multiple of its horizontal (Heisenberg) perimeter. This isoperimetric-type inequality exhibits different behavior in...

Random band matrices (RBM) are natural intermediate models to study eigenvalue statistics and quantum propagation in disordered systems, since they interpolate between mean-field type Wigner matrices and random Schrodinger operators. In particular...

We will give an overview of some of the developments in recent years dealing with the description of asymptotic states of solutions to semilinear evolution equations ("soliton resolution conjecture").

New results will be presented on damped...

Zero sets of Laplace eigenfunctions are called nodal sets. The talk will focus on propagation of smallness techniques, which are useful for estimates of the Hausdorff measure of the nodal sets.

A topological dynamical system $(X,T)$ is said to be Möbius disjointnes if \[\tag{$*$} \lim_{N\to\infty}\frac1N\sum_{n\leq N}f(T^nx)\mu(n)=0\] for all $f\in C(X)$ and $x\in X$ ($\mu$ stands for the classical Möbius function).Sarnak's conjecture from...