# Analysis Seminar

## Global existence and convergence of solutions to gradient systems and applications to Yang-Mills flow

## Stochastic quantization equations

## A Non-Isotropic Mechanism for the Formation of Trapped Surfaces

## On the Existence of Global Solutions of Certain Fluid Models

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).

## Conformal Invariants from Nodal Sets

## Hamiltonian Instability Driven by Recurrent Dynamics

## Calibrations of Degree Two and Regularity Issues

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-dimensional case where we will show a surprising connection with pseudo-holomorphic curves and an infinitesimal regularity result, namely the uniqueness of tangent cones

## Resonances for Normally Hyperbolic Trapped Sets

Resonances are complex analogs of eigenvalues for Laplacians on noncompact manifolds, arising in long time resonance expansions of linear waves. We prove a Weyl type asymptotic formula for the number of resonances in a strip, provided that the set of trapped geodesics is r-normally hyperbolic for large r and satisfies a pinching condition. Our dynamical assumptions are stable under small smooth perturbations and motivated by applications to black holes. We also establish a high frequency analog of resonance expansions.

## New Approximations of the Total Variation, and Filters in Image Processing

I will present new results concerning the approximation of the BV-norm by nonlocal, nonconvex, functionals. The original motivation comes from Image Processing. Numerous problems remain open. The talk is based on a joint work with H.-M. Nguyen.

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