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...
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
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...
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
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...
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...
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...