# Mathematical Physics

### Modular bootstrap, Segal's axioms and resolution of Liouville conformal field theory

Vincent Vargas and Rémi Rhodes

Liouville field theory was introduced by Polyakov in the eighties in the context of string theory. Liouville theory appeared there under the form of a 2D Feynman path integral, which can be thought of as a measure (or expectation value) over the...

### Towards Morse theory of dispersion relations

Gregory Berkolaiko

The question of optimizing an eigenvalue of a family of self-adjoint operators that depends on a set of parameters arises in diverse areas of mathematical physics.  Among the particular motivations for this talk are the Floquet-Bloch decomposition...

### Invariant Gibbs measures for the cubic nonlinear wave equation

In this talk, we prove the invariance of the Gibbs measure for the three-dimensional cubic nonlinear wave equation, which is also known as the hyperbolic Φ43-model.

In the first half of this talk, we illustrate our main objects and questions...

### Large Genus Asymptotics in Flat Surfaces and Hyperbolic Geodesics

In this talk we will describe the behaviors of flat surfaces and geodesics on hyperbolic surfaces, as their genera tend to infinity. We first discuss enumerative results that count the number of such surfaces or geodesics (which can be viewed as...

### An Introduction to Grassmann integrals with applications to statistical mechanics

Grassmann integrals are integrals over functions on an exterior algebra. In the "Gaussian" case they can be expressed as a determinant or Pfaffian.

These integral arise in two dimensional Ising models and random tilings or dimers.

W...

### Bounds on Maass spectra from holomorphic forms

I will discuss new constraints on the spectra of Maass forms on compact hyperbolic 2-orbifolds. The constraints arise from integrals of products of four functions in discrete series representations realized in L2(Γ∖G), where Γ is a cocompact lattice...

### Log-Sobolev inequality for near critical Ising and continuum φ4 measures

I will present results on Glauber dynamics of Ising models and continuum

φ4 measures.

For ferromagnetic Ising models, we show that the log-Sobolev constant satisfies a simple bound expressed only in terms of the susceptibility of the...

### An Introduction to Liouville Theory

Liouville Conformal Field Theory (LCFT) is an essential building block of Polyakov’s formulation of non critical string theory. Moreover, scaling limits of statistical mechanics models on random lattices (planar maps) are believed to be described by...

### Singularity formation in incompressible fluids

Tarek Elgindi
We discuss the problem of singularity formation for some of the basic equations of incompressible fluid mechanics such as the incompressible Euler equation and the surface quasi-geostrophic (SQG) equation. We begin by going over some of the...

### Functional inequalities and gradient flow for quantum evolution

Eric Carlen
We present joint work with Jan Maas showing that Quantum Markov semigroups satisfying a detailed balance condition are gradient flow for quantum relative entropy, and use this prove some conjectured inequalities arising in quantum information theory...