Analysis Seminar

I shall explain the structure of correlation functions for square-free numbers and describe a 'natural' dynamical system associated to them. Spectral analysis allows us to show that this system is metrically isomorphic to a translation on a compact...

I will discuss some recent work, joint with B. Pausader, on constructing global solutions of defocusing energy-critical nonlinear Schrodinger equations in periodic and semiperiodic settings.

Calibrated currents are a particular class of volume-minimizers and as such provide interesting explicit examples of solutions to Plateau's problem. Their role goes however much beyond that: they naturally appear when dealing with several geometric...

The Davenport-Heilbronn function (introduced by Titchmarsh) is a linear combination of the two L-functions with a complex character mod 5, with a functional equation of L-function type but for which the analogue of the Riemann hypothesis fails. In...

In this talk, we will present some recent results in the study of the nonlinear wave equation with cubic defocusing nonlinearity, describing the completion of a program to establish global well-posedness and scattering in the energy-supercritical...

The classical result on the uniqueness of black holes in GR, due to Hawking, which asserts that regular, stationary solutions of the Einstein vacuum equations must be isometric to an admissible black hole Kerr solution, has at its core a a highly...

For 2D Euler equation, we prove a double exponential lower bound on the vorticity gradient. We will also discus some further results on the singularity formation for other models.

Let $\Omega$ and $\tilde{\Omega}$ be domains in the hyperbolic plane with smooth boundary. Assume that both domains are uniformly convex, and have the same area. We show that there exists an area-preserving, orientation-preserving diffeomorphism $f...

If we deform a submanifold along its mean curvature vector, which is called mean curvature flow (MCF), the area will decrease most rapidly. Being Lagrangian is preserved along MCF in Kahler-Einstein manifolds. We can thus try to construct special...

We investigate the Bilinear Hilbert Transform in the plane and the pointwise convergence of bilinear averages in Ergodic theory, arising from Z^2 actions. Our techniques combine novel one and a half dimensional phase-space analysis with more...