Advances On Superelliptic Curves And Their Applications

Author : L. Beshaj,T. Shaska,E. Zhupa
Publisher : IOS Press
Page : 387 pages
File Size : 53,5 Mb
Release : 2015-07-16
Category : Computers
ISBN : 9781614995203

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Advances on Superelliptic Curves and Their Applications by L. Beshaj,T. Shaska,E. Zhupa Pdf

This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.

Author : Lubjana Beshaj,Tony Shaska
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 50,5 Mb
Release : 2019-02-26
Category : Curves, Algebraic
ISBN : 9781470442477

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Algebraic Curves and Their Applications by Lubjana Beshaj,Tony Shaska Pdf

This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.

Author : Andreas Malmendier,Tony Shaska
Publisher : American Mathematical Soc.
Page : 222 pages
File Size : 46,6 Mb
Release : 2018-04-03
Category : Arithmetical algebraic geometry
ISBN : 9781470428563

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Higher Genus Curves in Mathematical Physics and Arithmetic Geometry by Andreas Malmendier,Tony Shaska Pdf

This volume contains the proceedings of the AMS Special Session on Higher Genus Curves and Fibrations in Mathematical Physics and Arithmetic Geometry, held on January 8, 2016, in Seattle, Washington. Algebraic curves and their fibrations have played a major role in both mathematical physics and arithmetic geometry. This volume focuses on the role of higher genus curves; in particular, hyperelliptic and superelliptic curves in algebraic geometry and mathematical physics. The articles in this volume investigate the automorphism groups of curves and superelliptic curves and results regarding integral points on curves and their applications in mirror symmetry. Moreover, geometric subjects are addressed, such as elliptic 3 surfaces over the rationals, the birational type of Hurwitz spaces, and links between projective geometry and abelian functions.

Author : Diaraf Seck,Kinvi Kangni,Philibert Nang,Marie Salomon Sambou
Publisher : Springer Nature
Page : 525 pages
File Size : 45,6 Mb
Release : 2022-10-09
Category : Mathematics
ISBN : 9783031046162

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Nonlinear Analysis, Geometry and Applications by Diaraf Seck,Kinvi Kangni,Philibert Nang,Marie Salomon Sambou Pdf

This book gathers twenty-two papers presented at the second NLAGA-BIRS Symposium, which was held at Cap Skirring and at the Assane Seck University in Ziguinchor, Senegal, on January 25–30, 2022. The five-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometric analysis, geometric structures, dynamics, optimization, inverse problems, complex analysis, algebra, algebraic geometry, control theory, stochastic approximations, and modelling.

Author : Aaron Wootton,S. Allen Broughton,Jennifer Paulhus
Publisher : American Mathematical Society
Page : 366 pages
File Size : 53,5 Mb
Release : 2022-02-03
Category : Mathematics
ISBN : 9781470460259

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Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics by Aaron Wootton,S. Allen Broughton,Jennifer Paulhus Pdf

Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.

Author : Frederick Hoffman
Publisher : Springer Nature
Page : 491 pages
File Size : 49,8 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9783031529696

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Combinatorics, Graph Theory and Computing by Frederick Hoffman Pdf

Author : Jennifer S. Balakrishnan,Noam Elkies,Brendan Hassett,Bjorn Poonen,Andrew V. Sutherland,John Voight
Publisher : Springer Nature
Page : 587 pages
File Size : 51,6 Mb
Release : 2022-03-15
Category : Mathematics
ISBN : 9783030809140

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Arithmetic Geometry, Number Theory, and Computation by Jennifer S. Balakrishnan,Noam Elkies,Brendan Hassett,Bjorn Poonen,Andrew V. Sutherland,John Voight Pdf

This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 537 pages
File Size : 43,5 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9781108715775

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Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Author : Kohei Arai,Rahul Bhatia,Supriya Kapoor
Publisher : Springer
Page : 1295 pages
File Size : 44,9 Mb
Release : 2019-07-08
Category : Technology & Engineering
ISBN : 9783030228682

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Intelligent Computing by Kohei Arai,Rahul Bhatia,Supriya Kapoor Pdf

This book presents the proceedings of the Computing Conference 2019, providing a comprehensive collection of chapters focusing on core areas of computing and their real-world applications. Computing is an extremely broad discipline, encompassing a range of specialized fields, each focusing on particular areas of technology and types of application, and the conference offered pioneering researchers, scientists, industrial engineers, and students from around the globe a platform to share new ideas and development experiences. Providing state-of-the-art intelligent methods and techniques for solving real- world problems, the book inspires further research and technological advances in this important area.

Author : Colin Boyd
Publisher : Springer
Page : 614 pages
File Size : 53,8 Mb
Release : 2003-06-30
Category : Computers
ISBN : 9783540456827

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Advances in Cryptology — ASIACRYPT 2001 by Colin Boyd Pdf

The origins of the Asiacrypt series of conferences can be traced back to 1990, when the ?rst Auscrypt conference was held, although the name Asiacrypt was ?rst used for the 1991 conference in Japan. Starting with Asiacrypt 2000, the conference is now one of three annual conferences organized by the Inter- tional Association for Cryptologic Research (IACR). The continuing success of Asiacrypt is in no small part due to the e?orts of the Asiacrypt Steering C- mittee (ASC) and the strong support of the IACR Board of Directors. There were 153 papers submitted to Asiacrypt 2001 and 33 of these were accepted for inclusion in these proceedings. The authors of every paper, whether accepted or not, made a valued contribution to the success of the conference. Sending out rejection noti?cations to so many hard working authors is one of the most unpleasant tasks of the Program Chair. The review process lasted some 10 weeks and consisted of an initial refe- eing phase followed by an extensive discussion period. My heartfelt thanks go to all members of the Program Committee who put in extreme amounts of time to give their expert analysis and opinions on the submissions. All papers were reviewed by at least three committee members; in many cases, particularly for those papers submitted by committee members, additional reviews were obt- ned. Specialist reviews were provided by an army of external reviewers without whom our decisions would have been much more di?cult.

Author : Moti Yung
Publisher : Springer
Page : 630 pages
File Size : 50,9 Mb
Release : 2003-08-02
Category : Computers
ISBN : 9783540457084

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Advances in Cryptology - CRYPTO 2002 by Moti Yung Pdf

Crypto 2002, the 22nd Annual Crypto Conference, was sponsored by IACR, the International Association for Cryptologic Research, in cooperation with the IEEE Computer Society Technical Committee on Security and Privacy and the Computer Science Department of the University of California at Santa Barbara. It is published as Vol. 2442 of the Lecture Notes in Computer Science (LNCS) of Springer Verlag. Note that 2002, 22 and 2442 are all palindromes... (Don’t nod!) Theconferencereceived175submissions,ofwhich40wereaccepted;twos- missionsweremergedintoasinglepaper,yieldingthetotalof39papersaccepted for presentation in the technical program of the conference. In this proceedings volume you will ?nd the revised versions of the 39 papers that were presented at the conference. The submissions represent the current state of work in the cryptographic community worldwide, covering all areas of cryptologic research. In fact, many high-quality works (that surely will be published elsewhere) could not be accepted. This is due to the competitive nature of the conference and the challenging task of selecting a program. I wish to thank the authors of all submitted papers. Indeed, it is the authors of all papers who have made this conference possible, regardless of whether or not their papers were accepted. The conference program was also immensely bene?ted by two plenary talks.

Author : Pierre Charollois,Gerard Freixas i Montplet,Vincent Maillot
Publisher : Springer Nature
Page : 324 pages
File Size : 53,5 Mb
Release : 2021-05-17
Category : Mathematics
ISBN : 9783030652036

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Arithmetic L-Functions and Differential Geometric Methods by Pierre Charollois,Gerard Freixas i Montplet,Vincent Maillot Pdf

This book is an outgrowth of the conference “Regulators IV: An International Conference on Arithmetic L-functions and Differential Geometric Methods” that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are: • Additive polylogarithms • Analytic torsions • Chabauty-Kim theory • Local Grothendieck-Riemann-Roch theorems • Periods • Syntomic regulator The book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rössler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.

Author : Gary L. Mullen,Daniel Panario,Igor E. Shparlinski
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 53,8 Mb
Release : 2008
Category : Computers
ISBN : 9780821843093

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Finite Fields and Applications by Gary L. Mullen,Daniel Panario,Igor E. Shparlinski Pdf

This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.

Author : Kenneth H. Rosen
Publisher : CRC Press
Page : 1611 pages
File Size : 46,5 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351644051

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Handbook of Discrete and Combinatorial Mathematics by Kenneth H. Rosen Pdf

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 421 pages
File Size : 46,7 Mb
Release : 2020-04-02
Category : Mathematics
ISBN : 9781108715744

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Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.