Finite Simple Groups Thirty Years Of The Atlas And Beyond

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Finite Simple Groups Thirty Years Of The Atlas And Beyond

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Author : Manjul Bhargava
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-07-24

Finite Simple Groups Thirty Years Of The Atlas And Beyond written by Manjul Bhargava and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-24 with Biography & Autobiography categories.

Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.

Ever Evolving Groups

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Author : Alexander A. Ivanov
language : en
Publisher: Springer Nature
Release Date : 2025-07-02

Ever Evolving Groups written by Alexander A. Ivanov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-02 with Mathematics categories.

This book presents an original approach to the theory of finite groups, placing finite sporadic groups on an equal footing. It provides a nearly comprehensive overview of developments in the study of sporadic groups since the classification of finite simple groups was completed. Authored by one of the key contributors to these developments, a major theme of the book is the growing role that geometry has played in this story in the form of diagram geometries, amalgams, graph theory and “pushing up”. The chapters interweave various ideas and techniques applicable to all sporadic groups. Many of the results presented—several due to the author and collaborators—appear in book form for the first time. While much of the book describes developments from recent decades, it also includes significant new material, notably on the enigmatic Thompson group and the Monster. The final chapter explores connections to Majorana algebras and discusses some remarkable conjectures. A valuable addition to the literature on finite simple groups, this book will appeal to a wide audience, from advanced graduate students to researchers in group theory, combinatorics, finite geometry, coding theory, graph theory, and other mathematical fields that use group theory to study symmetries and structures.

Algebraic Combinatorics And The Monster Group

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Author : Alexander A. Ivanov
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17

Algebraic Combinatorics And The Monster Group written by Alexander A. Ivanov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-17 with Mathematics categories.

The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.

Finite Simple Groups

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Author : Manjul Bhargava
language : en
Publisher:
Release Date : 2017

Finite Simple Groups written by Manjul Bhargava and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Atlas of finite groups categories.

A mathematics conference partially based on Atlas of finite groups, by John H. Conway, et al. (Oxford University Press, 1985).

Surveys In Combinatorics 2021

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Author : Konrad K. Dabrowski
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-24

Surveys In Combinatorics 2021 written by Konrad K. Dabrowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-24 with Mathematics categories.

These nine articles provide up-to-date surveys of topics of contemporary interest in combinatorics.

The Computer Algebra System Oscar

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Author : Wolfram Decker
language : en
Publisher: Springer Nature
Release Date : 2025-01-30

The Computer Algebra System Oscar written by Wolfram Decker and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Mathematics categories.

This book presents version 1.0 of the new Computer Algebra System OSCAR. Written in Julia, OSCAR builds on and vastly extends four cornerstone systems: ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry. It offers powerful computational tools that transcend the boundaries of the individual disciplines involved. It is freely available, open source software. The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.

Endotrivial Modules

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Author : Nadia Mazza
language : en
Publisher: Springer
Release Date : 2019-05-25

Endotrivial Modules written by Nadia Mazza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-25 with Mathematics categories.

This is an in-depth report on the endotrivial modules, an important class of modular representations for finite groups. Following the historical development of the theory, the book starts with a review of the necessary definitions and some key examples. The main results obtained using traditional techniques are then presented, followed by more recent results such as the work of Grodal inspired by algebraic topology. In the last part of the book original methods are applied to obtain the group of endotrivial modules for certain very important groups. An accessible reference collecting half a century of research on endotrivial modules, this book will be of interest to researchers in algebra.

Inverse Galois Theory

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Author : Gunter Malle
language : en
Publisher: Springer
Release Date : 2018-07-27

Inverse Galois Theory written by Gunter Malle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-27 with Mathematics categories.

A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.

Representations Of Lie Algebras Quantum Groups And Related Topics

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Author : Naihuan Jing
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-21

Representations Of Lie Algebras Quantum Groups And Related Topics written by Naihuan Jing and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Mathematics categories.

This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.

Higher Genus Curves In Mathematical Physics And Arithmetic Geometry

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Author : Andreas Malmendier
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-04-03

Higher Genus Curves In Mathematical Physics And Arithmetic Geometry written by Andreas Malmendier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-03 with Mathematics categories.

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.