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Twelve Sporadic Groups
The 20 sporadics involved in the Monster, the largest sporadic group, constitute the Happy Family. This book is a leisurely and rigorous study of two of their three generations. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.
Vertex Operator Algebras, Number Theory and Related Topics
This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11–15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings center around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.
Recent Developments in Lie Algebras, Groups and Representation Theory
This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.
Finite Groups--coming of Age
These conference papers should dispel any post-classification pessimism about the future of the theory of finite simple groups. Having noted that the theory developed for the classification touches on so few other branches of mathematics, the editor focuses on research in finite simple groups not central to the classification and presents a broad context for the recent results in the field. The papers are aimed at researchers and graduate students in algebra. They pay special attention to current research in sporadic geometry, the Fischer-Griess Monster group, and moonshine. Though all the papers are of high research value, the following papers of unusual significance should be singled out: Frenkel, Lepowsky, and Meurman's construction of the Monster group $F_1$; Conway and Queen's computation of characters of $E_8({\bf C})$; Norton's proof of the uniqueness of the Monster; and Mason's exploration of moonshine.
Shape, Smoothness, and Invariant Stratification of an Attracting Set for Delayed Monotone Positive Feedback
This book contains recent results about the global dynamics defined by a class of delay differential equations which model basic feedback mechanisms and arise in a variety of applications such as neural networks. The authors describe in detail the geometric structure of a fundamental invariant set, which in special cases is the global attractor, and the asymptotic behavior of solution curves on it. The approach makes use of advanced tools which in recent years have been developed for the investigation of infinite-dimensional dynamical systems: local invariant manifolds and inclination lemmas for noninvertible maps, Floquet theory for delay differential equations, a priori estimates controlli...
Vertex Operator Algebras in Mathematics and Physics
Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.
An Introduction to Groups and Lattices
Rational lattices occur throughout mathematics, as in quadratic forms, sphere packing, Lie theory, and integral representations of finite groups. Studies of high-dimensional lattices typically involve number theory, linear algebra, codes, combinatorics, and groups. This book presents a basic introduction to rational lattices and finite groups and to the deep relationship between these two theories. Robert L. Griess, Jr. is a professor of mathematics at the University of Michigan. His various honors include a Guggenheim Fellowship, an invited lecture at the International Congress of Mathematicians, membership in the American Academy of Arts and Sciences, and the 2010 AMS Leroy P. Steele Prize...
Vertex Operators in Mathematics and Physics
James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the...
Facets of Algebraic Geometry
Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.
The Classification of Finite Simple Groups
Provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the 'even case', where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of 'noncharacteristic 2 type'.
