Compact Matrix Quantum Groups And Their Combinatorics
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Compact Matrix Quantum Groups and Their Combinatorics
Author: Amaury Freslon
language: en
Publisher: Cambridge University Press
Release Date: 2023-07-27
An organised step-by-step introduction to the theory of compact quantum groups, starting with examples coming from quantum physics, which stems from the basic undergraduate mathematics curriculum. Introducing more abstract concepts along the way when needed, the reader is led from the fundamentals of the theory to recent research results. The emphasis is put on the combinatorics underlying compact quantum groups, which is very elementary to describe but leads to profound results. This book includes many exercises to help students work through new concepts and ideas and consolidate their understanding. The theory itself is illustrated by an array of examples, some related to other fields of Mathematics such as free probability theory or graph theory. The book is intended for graduate students, motivated undergraduate students and researchers.
Künneth Geometry
Author: M. J. D. Hamilton
language: en
Publisher: Cambridge University Press
Release Date: 2023-12-21
This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses Künneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.
Inverse Problems and Data Assimilation
Author: Daniel Sanz-Alonso
language: en
Publisher: Cambridge University Press
Release Date: 2023-08-10
A clear and concise mathematical introduction to the subjects of inverse problems and data assimilation, and their inter-relations.