Analysis Seminar

Numerous manifestations of wave localization permeate acoustics, quantum physics, mechanical and energy engineering. It was used in construction of noise abatement walls, LEDs, optical devices, to mention just a few applications. Yet, no systematic...

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 discuss our results on global existence and convergence of solutions to the gradient flow equation for the Yang-Mills energy functional over a closed, four-dimensional, Riemannian manifolds: If the initial connection is close enough to a minimum...

Stochastic quantization equations are evolutionary PDEs driven by space-time white noises. They are proposed by physicists in the 80s as the natural dynamics associated to the (Euclidean) quantum field theories. We will discuss the recent progress...

I present a new, fully anisotropic, criterion for formation of trapped surfaces in vacuum obtained in collaboration with J. Luk and I. Rodnianski. We provide conditions on null data, concentrated in a neighborhood of a short null geodesic segment...

The talk is based on a recent work of M. Avdeeva (Princeton University), D. Li (IAS) and Ya. G. Sinai (Princeton University). We consider some new probability distributions related to the Mobius function and discuss their statistical properties. A...

I will discuss recent work on the global stability of the Euler-Maxwell equations in 3D (joint work with Guo and Pausader), and of the gravity water-wave system in 2D (joint work with Pusateri).

We study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a...

We present some novel approaches to the instability problem of Hamiltonian systems (in particular, the Arnold Diffusion problem). We show that, under generic conditions, perturbations of geodesic flows by recurrent dynamics yield trajectories whose...

Calibrated currents naturally appear when dealing with several geometric questions, some aspects of which require a deep understanding of regularity properties of calibrated currents. We will review some of these issues, then focusing on the two...