# analysis math-physics

Pavel Kurasov

### The nonlinear stability of the Schwarzschild metric without symmetry

Mihalis Dafermos

I will discuss an upcoming result proving the full finite-codimension non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region.

No symmetry is assumed. The...

### Cardy embedding of random planar maps

Nina Holden

A random planar map is a canonical model for a discrete random surface which is studied in probability theory, combinatorics, mathematical physics, and geometry. Liouville quantum gravity is a canonical model for a random 2D Riemannian manifold with...

### Extreme eigenvalue distributions of sparse random graphs

I will discuss the extreme eigenvalue distributions of adjacency matrices of sparse random graphs, in particular the Erd{\H o}s-R{\'e}nyi graphs $G(N,p)$ and the random $d$-regular graphs. For Erd{\H o}s-R{\'e}nyi graphs, there is a crossover in the...

### Unitary, Symplectic, and Orthogonal Moments of Moments

Emma Bailey

The study of random matrix moments of moments has connections to number theory, combinatorics, and log-correlated fields. Our results give the leading order of these functions for integer moments parameters by exploiting connections with Gelfand...

### On a universal limit conjecture for the nodal count statistics of quantum graphs

Lior Alon and Lior Alon

We consider Laplace eigenfunctions of a metric graph satisfying Neumann-Kirchhoff conditions on every vertex. The nodal count of a given eigenfunction is the number of points at which it vanishes. The nodal count of the n-th eigenfunction was shown...

### Billiards and Hodge theory

A polygon with rational angles can be unfolded and glued into a finite genus Riemann surface equipped with a flat metric and some singularities. The moduli space of all such structures carries an action of the group $\mathrm{PSL}(2,\mathbb R)$ and...

### Thermodynamical approach to the Markoff-Hurwitz equation

Michael Magee
I'll first introduce the Markoff-Hurwitz equation and explain how it plays a fundamental role in different areas of mathematics. The main result I'll discuss is a true asymptotic formula for the number of real points in a fixed orbit of the...

### Soliton resolution for energy critical wave and wave map equations

It is widely believed that the generic dynamics of nonlinear dispersive equations in the whole space is described by solitary waves and linear dispersions. More precisely, over large times, solutions tend to de-couple into solitary waves plus...