A bstract We study the statistics of the metric on Kähler moduli space in compactifications of
string theory on Calabi-Yau hypersurfaces in toric varieties. We find striking hierarchies in …

A bstract We investigate the analogy between the large N expansion in normal matrix
models and the asymptotic expansion of the determinant of the Hilb map, appearing in the …

We consider two-dimensional Coulomb gases on the Riemann sphere with determinantal or
Pfaffian structures, under external potentials that are invariant under rotations around the …

We provide a survey of results on the statistics of random sections of holomorphic line
bundles on K\" ahler manifolds, with an emphasis on the resulting asymptotics when a line …

We emphasize the close relationship between zeta function methods and arbitrary spectral
cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound …

The purpose of this article is to propose a new method to define and calculate path integrals
over metrics on a Kähler manifold. The main idea is to use finite dimensional spaces of …

We compute the first four coefficients of the asymptotic off-diagonal expansion in Shiffman
and Zelditch (J. Reine Angew. Math. 544: 181–222, 2002) of the Bergman kernel for the N-th …

The heat kernel on the symmetric space of positive definite Hermitian matrices is used to
endow the spaces of Bergman metrics of degree k on a Riemann surface M with a family of …

A bstract We study partition functions of random Bergman metrics, with the actions defined
by a class of geometric functionals known as 'stability functions'. We introduce a new stability …

This thesis presents original results in two domains of disordered statistical physics:
logarithmic correlated Random Energy Models (logREMs), and localization transitions in …