Research

I am interested in compact quantum groups, and their applications to quantum physics. There has been a lot of work here, and I am now attempting to review the known basic results on the subject, published or folklore, in a series of short books

1. Linear algebra and group theory
2. Complex Hadamard matrices and applications
3. Free quantum groups and related topics
4. Quantum permutations and lattice models
5. Quantum isometries and noncommutative geometry
...

with level ranging from undergraduate textbook to research monograph, organized as follows:

1 > 3 > 5
\/    \/
2 > 4

I started to work on this in 2019. I am currently done with 3, working on 2,5, and making a plan for 1,4. I will upload the final products here on my webpage, and on the standard scientific websites. With a bit of luck, hope to be done by 2022.