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The past few years have witnessed a remarkable crossover of string theoretical ideas from the abstract world of geometrical forms to the concrete experimental realm of condensed matter physics. The basis for this --- variously known as…
The thesis develops a systematic procedure to construct semi-classical gravitational duals from quantum state manifolds. Though the systems investigated are simple quantum mechanical systems without gauge symmetry many familiar concepts…
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an…
We introduce a general framework for generating dualities between categories of partial orders and categories of ordered Stone spaces; we recover in particular the classical Priestley duality for distributive lattices and establish several…
Necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Generalized conceptions of distances and dimensionality evaluation are…
We obtain the exact solution of the bond-percolation thresholds with inhomogenous probabilities on the square lattice. Our method is based on the duality analysis with real-space renormalization, which is a profound technique invented in…
Witten's topological B-model on a Calabi-Yau background is known to reproduce, in the open string sector, the derived category of coherent sheaves. When the target space is a complex torus, the topological model enjoys a non-geometric…
We describe topological gauge theories for which duality properties are encoded by construction. We study them for compact manifolds of dimensions four, eight and two. The fields and their duals are treated symmetrically, within the context…
In this lecture I review recent results on the use of Solvable Lie Algebras as an efficient description of the scalar field sector of supergravities in relation with their non perturbative structure encoded in the U-duality group. I also…
We give functorial recipes to get, out of any Hopf algebra over a field, two pairs of Hopf algebras which have some geometrical content. When the ground field has characteristic zero, the first pair is made by a function algebra over a…
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…
We study duality transformation and duality symmetry in the the electromagnetic-like charged p-form theories. It is shown that the dichotomic characterization of duality groups as $Z_2$ or SO(2) remains as the only possibilities but are now…
A duality of $\kappa$-normed topological vector spaces is defined and investigated. For such spaces the analog of the Mackey-Arens theorem is proved. There are investigated cases, when $\kappa$-normability of a topological vector space…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
We investigate computable metrizability of Polish spaces up to homeomorphism. In this paper we focus on Stone spaces. We use Stone duality to construct the first known example of a computable topological Polish space not homeomorphic to any…
A fundamental step towards studying string theory vacua, and, ultimately, their stability, is that of understanding the underlying mathematical structure of the QFT resulting from its dimensional reduction on Calabi-Yau (CY) manifolds, the…
The ternary extended contact relation was introduced in (Ivanova, 2020) as a more expressive counterpart of the standard binary contact relation. The class of Boolean algebras expanded with the relation was named Extended Contact Algebras…
Our purpose in this paper is to discuss criteria for the existence of a precise dual description of a cosmology. A number of exact descriptions exist for flat and anti de Sitter backgrounds and possibly for open FRW universes that nucleate…
Double sequence spaces have become a significant area of research within functional analysis due to their applications in various branches of mathematics and mathematical physics. In this study, we investigate Hahn double sequence space…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…