Analysis Seminar

We consider the Navier–Stokes equations posed on the half space, with Dirichlet boundary conditions. We give a direct energy based proof for the instantaneous space-time analyticity and Gevrey class regularity of the solutions, uniformly up to the...

A celebrated theorem of C.L. Siegel from 1929 shows that the multiplicity of eigenvalues for the Laplace eigenfunctions on the unit disk is at most two. More precisely, Siegel shows that positive zeros of Bessel functions are transcendental.

We...

We discuss two old questions of Landis concerning behavior of solutions of second order elliptic equations. The first one is on propagation of smallness for solutions from sets of positive measure, we answer this question and as a corollary prove an...

In the early 1920s, Loewner introduced a constructive approach to the Riemann mapping theorem that realized a conformal mapping as the solution to a differential equation. Roughly, the “input” to Loewner’s differential equation is a driving measure...

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...