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Finite simple groups : thirty years of The atlas and beyond / [edited by] Manjul Bhargava...[et al.].

By: Contributor(s): Material type: TextTextSeries: Contemporary mathematics ; 694.Publication details: Providence : American Mathematical Society, ©2017.Description: ix, 229 pages : illustrations ; 26 cmISBN:
  • 9781470436780 (pbk. : alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512c
Contents:
Moonshine and the meaning of life / Yang-Hui He and John McKay -- The Monster is fabulous / Simon P. Norton -- Majorana representation of the Monster group / A. A. Ivanov -- Letter to Donna Testerman / Jean-Pierre Serre -- Reliability and reproducibility of Atlas information / Thomas Breuer, Gunter Malle and E. A. O'Brien -- Characters and Brauer trees of the covering group of ²E₆(2) / Frank Lübeck -- Maximal subgroups of sporadic groups / Robert A. Wilson -- Construction of the Thompson Chain of subgroups of the Conway group [dot]O and complete graphs on /n/ letters / R. T. Curtis -- Conway's groupoid and its relatives / Nick Gill, Neil I. Gillespie, Cheryl E. Praeger and Jason Semeraro -- The subgroup structure of finite groups / Michael Aschbacher -- Some remarks on maximal subgroups of finite classical groups / Kay Magaard -- Toward a classification of endotrivial modules / Jon F. Carlson -- Some remarks on global/local conjectures / Gabriel Navarro -- Minuscule weights and Chevalley groups / Meinolf Geck -- A method for building permutation representations of finitely presented groups / Gabriele Nebe, Richard Parker and Sarah Rees -- Character ratios for finite groups of Lie type, and applications / Martin W. Liebeck -- Conjugacy classes, growth and complexity / Aner Shalev -- Permutation groups where non-trivial elements have few fixed points / Rebecca Waldecker.
Summary: This volume contains the proceedings of the international conference Finite Simple Groups: Thirty Years of the Atlas and Beyond Celebrating the Atlases and Honoring John Conway, which was held from November 2-5, 2015, at Princeton University, Princeton, New Jersey.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.
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Includes bibliographical references.

Moonshine and the meaning of life / Yang-Hui He and John McKay --
The Monster is fabulous / Simon P. Norton --
Majorana representation of the Monster group / A. A. Ivanov --
Letter to Donna Testerman / Jean-Pierre Serre --
Reliability and reproducibility of Atlas information / Thomas Breuer, Gunter Malle and E. A. O'Brien --
Characters and Brauer trees of the covering group of ²E₆(2) / Frank Lübeck --
Maximal subgroups of sporadic groups / Robert A. Wilson --
Construction of the Thompson Chain of subgroups of the Conway group [dot]O and complete graphs on /n/ letters / R. T. Curtis --
Conway's groupoid and its relatives / Nick Gill, Neil I. Gillespie, Cheryl E. Praeger and Jason Semeraro --
The subgroup structure of finite groups / Michael Aschbacher --
Some remarks on maximal subgroups of finite classical groups / Kay Magaard --
Toward a classification of endotrivial modules / Jon F. Carlson --
Some remarks on global/local conjectures / Gabriel Navarro --
Minuscule weights and Chevalley groups / Meinolf Geck --
A method for building permutation representations of finitely presented groups / Gabriele Nebe, Richard Parker and Sarah Rees --
Character ratios for finite groups of Lie type, and applications / Martin W. Liebeck --
Conjugacy classes, growth and complexity / Aner Shalev --
Permutation groups where non-trivial elements have few fixed points / Rebecca Waldecker.

This volume contains the proceedings of the international conference Finite Simple Groups: Thirty Years of the Atlas and Beyond Celebrating the Atlases and Honoring John Conway, which was held from November 2-5, 2015, at Princeton University, Princeton, New Jersey.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.

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