# Year: 2022

## A magic approach to octonionic Rosenfeld spaces

In his study on the geometry of Lie groups, Rosenfeld postulated a strict relation between all real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces over the (rank-2) tensor product of Hurwitz algebras taken with appropriate conjugations. Unfortunately, the procedure carried out by Rosenfeld was not rigorous, since many of […]

## Algebraic Morphology of DNA–RNA Transcription and Regulation

Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. In this paper, we describe the algebraic geometry of both TFs and miRNAs thanks to group theory. In TFs, the generator of the group is a DNA-binding domain while, in miRNAs, the generator is the seed of […]

## Fricke Topological Qubits

We recently proposed that topological quantum computing might be based on SL(2,C) representations of the fundamental group π1(S3\K) for the complement of a link K in the three-sphere. The restriction to links whose associated SL(2,C) character variety V contains a Fricke surface κd=xyz−x2−y2−z2+d is desirable due to the connection of Fricke spaces to elementary topology. Taking K as the Hopf link L2a1, one of the three arithmetic two-bridge links (the […]

## DNA Sequence and Structure under the Prism of Group Theory and Algebraic Surfaces

Taking a DNA sequence, a word with letters/bases A, T, G and C, as the relation between the generators of an infinite group π, one can discriminate between two important families: (i) the cardinality structure for conjugacy classes of subgroups of π is that of a free group on one to four bases, and the […]

## Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing

The concrete realization of topological quantum computing using low-dimensional quasiparticles, known as anyons, remains one of the important challenges of quantum computing. A topological quantum computing platform promises to deliver more robust qubits with additional hardware-level protection against errors that could lead to the desired large-scale quantum computation. We propose quasicrystal materials as such a […]

## Character Varieties and Algebraic Surfaces for the Topology of Quantum Computing

It is shown that the representation theory of some finitely presented groups thanks to their $SL_2(\mathbb{C})$ character variety is related to algebraic surfaces. We make use of the Enriques-Kodaira classification of algebraic surfaces and the related topological tools to make such surfaces explicit. We study the connection of $SL_2(\mathbb{C})$ character varieties to topological quantum computing […]

## Synthesis of the Ti-Zr-Ni alloys by the “hydride cycle” method

A comprehensive study of the technical parameters and conditions for the synthesis of ternary alloys in the Ti-Zr-Ni system by the “hydride cycle” method was carried out. The influence on the synthesis process of such parameters as: temperature and annealing time, heating rate, cooling conditions, material composition, dispersion, hydrogen content in the hydrides used, the […]