Proud to Publish: Quantum Riemannian Geometry

In our Proud to Publish series we talk to our book editors about the books they were most proud to publish, commission or work on in the past year. In this article Dr Rémi Lodh, Senior Editor for Mathematics Books and mathematician himself, tells us about a book he’s particularly proud of.

Thinking about books you’ve published in 2020, which one are you most proud of?

It's hard to choose, but probably the book Quantum Riemannian Geometry by Edwin Beggs and Shahn Majid. This is a book on some mathematics related to quantum physics, and includes 'real world' applications to things like quantum spacetime.

Why is this your personal 2020 highlight?

This is one of the few significant books on the subject since the appearance of Fields medallist Alain Connes’ Noncommutative Geometry in 1994. Noncommutative geometry is an abstract form of geometry where the multiplication of coordinates depends on the actual order in which they are multiplied (like what happens with matrices). Although this may seem unnatural at first, it turns out that a lot of familiar geometric machinery can be built in this setting. Analogy can be a very powerful tool in mathematics—when it works!

But the book doesn't merely repeat the established theory: it presents an original approach, different to the previous books, and covers a range of results that have never appeared in books before.

Lastly, this book is published in the Grundlehren der mathematischen Wissenschaften, the original yellow book series and oldest mathematics series at Springer. Some of the most famous books in all of mathematics have appeared in this series.

Is there anything else you want to share about this title?

Although he almost certainly has a nice office in his department, prior to the pandemic Shahn Majid could usually be found working at his favourite café in Hampstead, North London. He would receive doctoral students and collaborators there, and I would go there to meet him and Edwin Beggs to discuss the book. This may seem somewhat eccentric, but in fact there's a long tradition of doing science and mathematics in coffee houses in London, going back to the 17th century with Newton, de Moivre, Hooke, Wren, and others.

Click here for more information about this and other titles in our Mathematics & Statistics collection. To add this title to your library contact us here.

If you are interested in publishing Mathematics books with us, please contact Dr Rémi Lodh.

About the authors

Edwin J. Beggs studied mathematics at Churchill college Cambridge, moving to St Catherine’s college Oxford to study for a DPhil under the supervision of Graeme Segal, finishing in 1988. He became a research assistant working with David Evans on operator algebras (giving a formula for the real rank of matrix valued functions) in Swansea and was appointed to a lectureship there. He has worked with Peter Johnson, finding the inverse scattering method for solitons in affine Toda field theory. He has worked with various co-authors on noncommutative differential geometry, introducing noncommutative sheaf theory, noncommutative complex structures and bar categories as well as working on bimodule connections and quantum Riemannian geometry. He also works on physics and computation in computer science.

Shahn Majid graduated from Cambridge, including Part III of the mathematics tripos, followed by a PhD at Harvard in 1988. After a year in Swansea, he spent ten years in DAMTP in Cambridge before moving to Queen Mary. He was one of the pioneers of the modern theory of Hopf algebras or quantum groups, introducing in his PhD thesis one of the two main classes at the time, the bicrossproduct ones associated to Lie group factorisations. Other results include the earliest models of quantum spacetime with quantum symmetry, the theory of Hopf algebras in braided categories and the dual/centre of a monoidal category. He was one of the co-authors of the theory of quantum principal bundles and introduced a frame bundle approach to quantum Riemannian geometry. In recent years he has been working on the bimodule approach with a view to quantum gravity.