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Axioms
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Advances in Algebraic Geometry
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Advances in Algebraic Geometry

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".

Deadline for manuscript submissions: closed (20 May 2023) | Viewed by 2259

Special Issue Editors

Prof. Dr. Elena Guardo

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 6, 95100 Catania, Italy
Interests: commutative algebra; algebraic geometry, multilinar algebra; computer algebra; combinatorics; graph theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Luca Chiantini

E-Mail Website
Guest Editor
Department of Mathematical and Computer Sciences, University of Siena, Pian dei Mantellini, 44, 53100 Siena, Italy
Interests: algebraic geometry; projective geometry; multilinar algebra; commutative algebra; computer algebra; algebraic statistics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Edoardo Ballico

E-Mail Website
Guest Editor
Department of Mathematics, University of Trento, Via Sommarive 14, 38123 Trento, Italy
Interests: algebraic geometry; projective geometry; multilinar algebra; commutative algebra

Special Issue Information

Dear Colleagues,

Algebraic geometry is a branch of mathematics that, classically, studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

The aim of this Special Issue, which is devoted mainly to algebraic geometry, is to collect recent noteworthy results and original research focusing on the latest progress and developments in this research area and its applications. We hope that this Special Issue will provide a good platform for researchers in different areas of algebraic geometry to come together and exchange ideas on how we can further develop and apply algebraic geometry. Only high-quality papers will be accepted for publication.

We look forward to receiving your contribution.

Prof. Dr. Elena Guardo
Prof. Dr. Luca Chiantini
Prof. Dr. Edoardo Ballico
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Algebraic Varieties;
  • Vector Bundles Over Projective Varieties;
  • Symbolic Computation;
  • Geometric Computation;
  • Vectors; Matrix;
  • Tensor Analysis;
  • Combinatorial Algebraic Geometry.

Published Papers (1 paper)

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Research

12 pages, 1404 KiB  
Article
SL(2,C) Scheme Processing of Singularities in Quantum Computing and Genetics
by Michel Planat, Marcelo M. Amaral, David Chester and Klee Irwin
Axioms 2023, 12(3), 233; https://doi.org/10.3390/axioms12030233 - 23 Feb 2023
Cited by 2 | Viewed by 1553
Abstract
Revealing the time structure of physical or biological objects is usually performed thanks to the tools of signal processing such as the fast Fourier transform, Ramanujan sum signal processing, and many other techniques. For space-time topological objects in physics and biology, we propose [...] Read more.
Revealing the time structure of physical or biological objects is usually performed thanks to the tools of signal processing such as the fast Fourier transform, Ramanujan sum signal processing, and many other techniques. For space-time topological objects in physics and biology, we propose a type of algebraic processing based on schemes in which the discrimination of singularities within objects is based on the space-time-spin group SL(2,C). Such topological objects possess an homotopy structure encoded in their fundamental group, and the related SL(2,C) multivariate polynomial character variety contains a plethora of singularities somehow analogous to the frequency spectrum in time structures. Our approach is applied to a model of quantum computing based on an Akbulut cork in exotic R4, to an hyperbolic model of topological quantum computing based on magic states and to microRNAs in genetics. Such diverse topics reveal the manifold of possibilities of using the concept of a scheme spectrum. Full article
(This article belongs to the Special Issue Advances in Algebraic Geometry)
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