# Analysis Seminar

### Local Dissipation of Energy for Continuous Incompressible Euler Flows

Phillip Isett

I will discuss the construction of continuous solutions to the incompressible Euler equations that exhibit local dissipation of energy and the surrounding motivations. A significant open question, which represents a strong form of the Onsager...

### Geodesics and Laplace spectrum on 3D contact sub-Riemannian manifolds: the Reeb flow

Yves Colin de Verdière

Joint work with Luc Hillairet (Orléans) and Emmanuel Trélat (Paris). A 3D closed manifold with a contact distribution and a metric on it carries a canonical contact form. The associated Reeb flow plays a central role for the asymptotics of the...

### The Schrodinger equations as inspiration of beautiful mathematics

In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of...

### Eigenfunction concentration via geodesic beams

A vast array of physical phenomena, ranging from the propagation of waves to the location of quantum particles, is dictated by the behavior of Laplace eigenfunctions. Because of this, it is crucial to understand how various measures of eigenfunction...

### Korevaar-Schoen energy revisited

Nicola Gigli

Korevaar and Schoen introduced, in a seminal paper in 1993, the notion of `Dirichlet energy’ for a map from a smooth Riemannian manifold to a metric space. They used such concept to extend to metric-valued maps the regularity theory by Eells-Sampson...

### Mean curvature flow in high co-dimension

William Minicozzi

Mean curvature flow (MCF) is a geometric heat equation where a submanifold evolves to minimize its area. A central problem is to understand the singularities that form and what these imply for the flow. I will talk about joint work with Toby Colding...

### From hyperbolic billiards to statistical physics

Consider a point particle flying freely on the torus and elastically bouncing back from the boundary of fixed smooth convex obstacles. This is the celebrated Sinai billiard, a rare example of a deterministic dynamical system where rigorous results...

### Long time dynamics of 2d Euler and nonlinear inviscid damping

In this talk, we will discuss some joint work with Alexandru Ionescu on the nonlinear inviscid damping near point vortex and monotone shear flows in a finite channel. We will put these results in the context of long time behavior of 2d Euler...

### Yang-Mills Instantons, Quivers and Bows

The study of hyperkaehler manifolds of lowest dimension (and of gauge theory on them) leads to a chain of generalizations of the notion of a quiver: quivers, bows, slings, and monowalls. This talk focuses on bows, their representations, and...

### Mean-Field limits for Coulomb-type dynamics

Sylvia Serfaty

We consider a system of NN particles evolving according to the gradient flow of their Coulomb or Riesz interaction, or a similar conservative flow, and possible added random diffusion. By Riesz interaction, we mean inverse power ss of the distance...
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