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Introduction to Vertex Operator Algebras and Their Representations
* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
Vertex Operator Algebras and the Monster
This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
The Handbook of Historical Sociolinguistics
Written by an international team of leading scholars, this groundbreaking reference work explores the nature of language change and diffusion, and paves the way for future research in this rapidly expanding interdisciplinary field. Features 35 newly-written essays from internationally acclaimed experts that reflect the growth and vitality of the burgeoning area of historical sociolinguistics Examines how sociolinguistic theoretical models, methods, findings, and expertise can be used to reconstruct a language's past in order to explain linguistic changes and developments Bridges the gap between the past and the present in linguistic studies Structured thematically into sections exploring: origins and theoretical assumptions; methods for the sociolinguistic study of the history of languages; linguistic and extra-linguistic variables; historical dialectology, language contact and diffusion; and attitudes to language
Lie Algebras and Related Topics
Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
Algebraic Combinatorics and the Monster Group
Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics
This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.
Analytic Number Theory, Modular Forms and q-Hypergeometric Series
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Lie Groups, Number Theory, and Vertex Algebras
This volume contains the proceedings of the conference Representation Theory XVI, held from June 25–29, 2019, in Dubrovnik, Croatia. The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three main topics of these articles are Lie theory, number theory, and vertex algebras.
Keys to the History of English
This volume brings together contributions selected from papers delivered at the 21st International Conference on English Historical Linguistics (ICEHL, Leiden 2021). The contributions deal with various aspects of English language across time and geographical space, shedding light on both long-term developments and singular documents of particular linguistic interest. A wide range of methodologies are represented, including corpus linguistics, acoustic phonetics and philology. Chapters showcase work on syntax and word order (parataxis and hypotaxis from Old to Late Modern English; left-dislocation in Old English; do-support in Scots), diachronic linguistic change (phonological developments of...
Number Theory
This book contains proceedings presented at the fourth Canadian Number Theory Association conference held at Dalhousie University in July 1994. The invited speakers focused on analytic, algebraic, and computational number theory. The contributed talks represented a wide variety of areas in number theory.
