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This thesis is framed within the field of Mathematical Relativity and is organized into six chapters. After an introduction to the topic in Chapter 1, Chapter 2 reviews and further develops the formalism of hypersurface data, which provides…

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…

In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second order differential equations on a half-line. Our goal is to extend the classical resultss developed in the work of…

In this survey we show how to produce asymptotics of determinants of structured matrices using operator theory methods. We describe the asymptotics for finite Toeplitz matrices, finite Toeplitz plus Hankel matrices and generalizations of…

In this thesis my papers hep-th/0104190, hep-th/0310214, hep-th/0405072 and hep-th/0406065 are put into context. The thesis is mainly focused on noncommutative field theory and string theory, so results in the papers that are not related to…

We study structurable algebras of skew-dimension one. We present two different equivalent constructions for such algebras: one in terms of non-linear isotopies of cubic norm structures, and one in terms of hermitian cubic norm structures.…

This thesis is concerned with a realisation of topological theories in terms of statistical models known as Calabi-Yau crystals. The thesis starts with an introduction and review of topological field and string theories. Subsequently…

In the first part of this paper we give an elementary proof of the fact that if an infinite matrix $A$, which is invertible as a bounded operator on $\ell^2$, can be uniformly approximated by banded matrices then so can the inverse of $A$.…

Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…

In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied…

This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…

Many of today's problems require techniques that involve the solution of arbitrarily large systems $A\mathbf{x}=\mathbf{b}$. A popular numerical approach is the so-called Greedy Rank-One Update Algorithm, based on a particular tensor…

We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed…

The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…

We define the Dunkl and Dunkl-Heckman operators in infinite number of variables and use them to construct the quantum integrals of the Calogero-Moser-Sutherland problems at infinity. As a corollary we have a simple proof of integrability of…

Matrix models have wide applications in nuclear theory, condensed matter theory and quantum field theory. I discuss supersymmetric extensions of matrix models and their applications to branched polymers, the meander problem, and…

This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…

The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns…

These three topics are an attempt to explicate some curiosities of the inverse problem of representation theory (i.e. having a set of operators to describe the "correct" algebraic object, which is represented by them) on simple examples…

This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…