Vertex Operator Algebras, Number Theory and Related Topics

The volume highlights recent developments in vertex operator algebras,number theory,and related topics,including 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. It contains original contributions and surveys on important topics,with open problems from leading experts in the field.

Format: Paperback / softback
Length: 268 pages
Publication date: 30 September 2020
Publisher: American Mathematical Society

The captivating realm of mathematics continues to flourish with the exploration of vertex operator algebras, vector-valued modular forms, and finite group theory. These mathematical disciplines offer a rich tapestry of ideas and theories that have the potential to revolutionize our understanding of the world. In recent years, there has been a remarkable resurgence of interest in moonshine-related mathematics, particularly concerning the Mathieu group and other fascinating groups. This resurgence has brought forth a renewed vigor and excitement in the field, as researchers delve deeper into the intricate structures and properties of these mathematical entities.

Moreover, the role of algebraic geometry has become increasingly significant in these mathematical pursuits. Algebraic geometry provides a powerful framework for studying complex geometric structures and their mathematical relationships. It has played a pivotal role in the development of irrational vertex operator algebras, which are a branch of mathematics that combines the principles of vertex operator algebras with the techniques of algebraic geometry.

One of the most exciting developments in the field of vertex operator algebras is the study of quantum groups. Quantum groups are a generalization of classical Lie groups, and they have been used to study a wide range of physical phenomena, including quantum mechanics, superconductivity, and the theory of relativity. Researchers have made significant progress in understanding the properties of quantum groups and their applications to various fields of science.

In addition to the theoretical advancements, there has been a growing interest in applying vertex operator algebras and vector-valued modular forms to solve practical problems in mathematics and physics. For example, these mathematical tools have been used to study the behavior of complex systems, such as the stock market, the weather, and the behavior of particles in the universe. They have also been used to develop new algorithms for solving optimization problems and for analyzing data.

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, provide a comprehensive overview of the latest research in these fields. The conference brought together leading researchers from around the world, and the contributions presented therein offer original insights and perspectives on the most pressing issues in vertex operator algebras, vector-valued modular forms, and finite group theory.

The conference proceedings are organized into several sections, including vertex operator algebras, vector-valued modular forms, and number theory. Each section includes a series of research papers that explore the latest developments in these areas. The papers cover a wide range of topics, from the theoretical foundations of vertex operator algebras to their applications to various fields of science.

One of the highlights of the conference proceedings is the survey section, which provides an overview of some of the most important topics relevant to these fields. The surveys cover a wide range of topics, from the history of vertex operator algebras to their connections to other areas of mathematics and physics. They also include a discussion of open problems and future research directions in these areas.

In conclusion, the mathematics of vertex operator algebras, vector-valued modular forms, and finite group theory continues to be a vibrant and dynamic field of research. 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 of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held at California State University, Sacramento, provide a valuable resource for researchers and scholars interested in these fields. The contributions presented therein offer original insights and perspectives on the latest research in these areas, and they will undoubtedly contribute to the further development of these mathematical disciplines.

Weight: 486g
Dimension: 181 x 255 x 17 (mm)
ISBN-13: 9781470449384