A bstract We carry out a numerical study of the spinless modular bootstrap for conformal field
theories with current algebra U (1) c× U (1) c, or equivalently the linear programming bound …

We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds
and orbifolds in three dimensions, including the standard Laplace-Beltrami operator on …

Let $\mathcal {M} _g $ be the moduli space of hyperbolic surfaces of genus $ g $ endowed
with the Weil-Petersson metric. In this paper, we show that for any $\epsilon> 0$, as …

We adapt linear programming methods from sphere packings to closed hyperbolic surfaces
and obtain new upper bounds on their systole, their kissing number, the first positive …

In this article, for any $ n\geq 4$ we construct a sequence of compact hyperbolic $ n $-
manifolds $\{M_i\} $ with number of systoles at least as $\mathrm {vol}(M_i)^{1+\frac {1}{3n …

Based on periodic orbit theory we address the individual-system versus ensemble
interpretation of quantum gravity from a quantum chaos perspective. To this end we show …

We study the systole of a model of random hyperbolic 3-manifolds introduced by Petri and
Raimbault, answering a question posed in that same article. These are compact manifolds …

In this article we construct a sequence $\{M_i\} $ of non compact finite volume hyperbolic $3
$-manifolds whose kissing number grows at least as $\mathrm {vol}(M_i)^{\frac {31}{27} …

We prove a sharp upper bound on the number of shortest cycles contained inside any
connected graph in terms of its number of vertices, girth, and maximal degree. Equality holds …

In this thesis, we will mainly discuss two types of related questions. The first of these
concerns extremal problems in hyperbolic geometry. An example of such a question is: what …