Related papers: Holonomy spin foam models: Asymptotic geometry of …

An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…

We show that the quantum geometry of the Fermi surface can be numerically described by a 3-dimensional discrete quantum manifold. This approach not only avoids singularities in the Fermi sea, but it also enables the precise computation of…

In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored. After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert…

For a 3-manifold M and a subsurface $X$ of the boundary of M with empty or incompressible boundary we use surgery to identify a graph whose vertices are disks with boundary in X and which is quasi-isometrically embedded in the curve graph…

In [17], Labourie initiated the study of the dynamical properties of the space of $k$-surfaces, that is, suitably complete immersed surfaces of constant extrinsic curvature in $3$-dimensional manifolds, which he presented as a…

We study the set of curvature functions which a given compact manifold with boundary can possess. First, we prove that the sign demanded by the Gauss-Bonnet Theorem is a necessary and sufficient condition for a given function to be the…

The effect of an atomically sharp impenetrable interface on the spin splitting of the spectrum of two-dimensional electrons in heterostructures based on (001) III-V compounds has been analyzed. To this end, the single band Hamiltonian…

We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…

We study properties of spectral minimal partitions of metric graphs within the framework recently introduced in [Kennedy et al, Calc. Var. 60 (2021), 61]. We provide sharp lower and upper estimates for minimal partition energies in…

This thesis is devoted to the study of 3-dimensional quantum gravity as a spin foam model and group field theory. In the first part of this thesis, we review some general physical and mathematical aspects of 3-dimensional gravity, focusing…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

We consider continuous and discrete (1+1)-dimensional wetting models which undergo a localization/delocalization phase transition. Using a simple approach based on Renewal Theory we determine the precise asymptotic behavior of the partition…

We are concerned with stochastic processes on surfaces in three-dimensional contact sub-Riemannian manifolds. Employing the Riemannian approximations to the sub-Riemannian manifold which make use of the Reeb vector field, we obtain a second…

Inspired by the works of Dewar, Murty and Kot\v{e}\v{s}ovec, we establish some useful theorems for asymptotic formulas. As an application, we obtain asymptotic formulas for the numbers of skew plane partitions and cylindric partitions. We…

Partition functions arise in statistical physics and probability theory as the normalizing constant of Gibbs measures and in combinatorics and graph theory as graph polynomials. For instance the partition functions of the hard-core model…

I discuss how to impose causality on spin-foam models, separating forward and backward propagation, turning a given triangulation to a 'causal set', and giving asymptotically the exponential of the Regge action, not a cosine. I show the…

The aim of this work is to present a general theory of coset models G/H in which different left and right actions of H on G are gauged. Our main results include a formula for their modular invariant partition function, the construction of a…

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large…

In this work we study a Spin Foam model for 4d Riemannian gravity, and propose a new way of imposing the simplicity constraints that uses the recently developed holomorphic representation. Using the power of the holomorphic integration…

We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…