Related papers: Non-perturbative data for Weil-Petersson volumes a…
The Gromov-Wasserstein (GW) problem, a variant of the classical optimal transport (OT) problem, has attracted growing interest in the machine learning and data science communities due to its ability to quantify similarity between measures…
A brief review is given of the recent solution of a non-compact CFT describing a NS-supported pp-wave background. We will first explain how to compute the three and four-point correlators using current algebra techniques, thereby showing…
The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some…
We employ the massive gravity approach to stress-tensor deformations in a variety of scenarios, obtaining novel results and establishing new connections. Starting with perturbation theory, we show that the addition of $\text{tr}…
In this thesis, we consider two approaches to the study of correlation functions in one-dimensional defect Conformal Field Theories (dCFT$_1$), in particular those defined by 1/2-BPS Wilson line defects in the three- and four-dimensional…
In this thesis, we discuss some of the applications of cosmological perturbation theory in the late universe. We begin by reviewing the tools used to understand the standard model of cosmology theoretically and to compute its observational…
We show here how Renormalized Perturbation Theory (RPT) calculations applied to the quasi-linear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly…
We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two point correlation and the pair velocity for Gaussian initial conditions in a critical density matter dominated cosmological…
Topological data analysis is becoming a popular way to study high dimensional feature spaces without any contextual clues or assumptions. This paper concerns itself with one popular topological feature, which is the number of…
We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such…
We construct a two-parameter four-dimensional non-BPS NS-NS smooth microstate solution that asymptotes to flat spacetime with a linear dilaton in type II superstring theory. From the microscopic point of view, the background is made out of…
Perturbative and non-perturbative results are presented on the renormalization constants of the quark field and the vector, axial-vector, pseudoscalar, scalar and tensor currents. The perturbative computation, carried out at one-loop level…
Since any string theory involves a path integration on the world-sheet metric, their partition functions are volume forms on the moduli space of genus g Riemann surfaces M_g, or on its super analog. It is well known that modular invariance…
We consider a general class of spin systems with potentially unbounded real-valued spins, defined via a single-site potential with super-Gaussian tails on general graphs, allowing for both short- and long-range interactions. This class…
We present in this paper a differential version of Mirzakhani's recursion relation for the Weil-Petersson volumes of the moduli spaces of bordered Riemann surfaces. We discover that the differential relation, which is equivalent to the…
We develop a geometric criterion that unambiguously characterizes and also provides a systematic and effective computational procedure for finding all the residual symmetries of any gravitational Ansatz . We apply the criterion to several…
It is shown that a first-order relativistic perturbation theory for the open, flat or closed Friedmann-Lemaitre-Robertson-Walker universe admits one, and only one, gauge-invariant quantity which describes the perturbation to the energy…
This note is based on a talk given by one of the authors (S. D.) at the "Rencontres Math\'ematiques de Glanon", held in Glanon in July 2004. We will first introduce the BTZ black hole, solution of Einstein's gravity in 2+1 dimensions, and…
We argue that for a large class of N=1 supersymmetric gauge theories the effective superpotential as a function of the glueball chiral superfield is exactly given by a summation of planar diagrams of the same gauge theory. This perturbative…
The Weil-Petersson volume of genus-g hyperbolic surfaces with geodesic boundaries is known since work of Mirzakhani to be polynomial in the boundary lengths. We provide a bijective proof of this fact in the genus-0 case in the presence of a…