Lectures on Tensor Categories and Modular Functors (University Lecture Series) by Bojko Bakalov (PDF)

Description

This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book has been carefully written exposing the subject of tensorial categories and their applications, these notes are correctly illustrated and can be. consider self contained. I recommend this book for anyone interested in getting started on this topic.

⭐I’m a physicist, and therefore interested in the applications of this subject to Quantum Computing. I expected to find a mathematician’s account hard going, but this book is very well organized and readable. To get a complete picture, I found it useful to pair it with “Topological Quantum computing” by Zhenghan Wang, and also to read the standalone paper “On an inner product in Modular Tensor Categories” by Kirillov.

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