This page contains a slightly more detailed presentation of my research.
It is intended for the curious reader, or for prospective graduate
students / postdocs. For details on my publications, grants (JSPS here),
teaching activities, graduate supervision activity, CV, follow this link.
For rather well maintained databases of my professional activities, scroll
down to [Open access/Subscription only access] of this
page .

In Kyoto, I am a member of the operator algebra group. Together with Yuki
Arano, Yusuke Isono, Masaki Izumi, Narutaka Ozawa, we organize the Kyoto
Operator Algebra Seminar (KOAS).

I keep close ties to the probability group in Kyoto too. Many of my
collaborators and visitors have are primarily probabilists and interact
with this group or speak at the probability
seminar.

Some people consider me as a probabilist or a mathematical physicist. I
am actually on the Editorial Board of general
mathematics journals, probability journals and mathematical physics
journals.

My primary research area is Random
Matrix Theory. Some view it as a branch probability theory, others
as mathematical physics. It is known to have close connections to
combinatorics, representation theory, operator algebras, applied
mathematics, integrable systems, algebraic geometry, number theory, etc. I
am also involved in Free
Probability Theory, especially in its applications.

I am also interested in Operator Algebras and Representation Theory. In
the past, I have devoted lots of time in the study of quantum groups.
Finally, I enjoy working on problems in mathematical Quantum Information
Theory.

Some topics to which I contributed (in a more or less choronological
order):
the Weingarten
calculus. Calculating the Haar measure on general compact quantum groups.
Covergence of general matrix integrals. Higher order freeness. The Connes
Embedding problem. The Horn problem in a general finite von Neumann
algebra. Strong asymptotic freeness for unitary random matrices. The
Minimum Output Entropy additivity problem. Alon's generalized conjecture.
Equivariant entanglment detection. Bound entanglement.

## Contact

- email
- coll
*REMOVETHISTEXT*ins@math.k*y*oto-u.ac.jp
- address
- Department of Mathematics, Graduate School of Science,
- Kyoto University, Kyoto 606-8502, Japan
- Tel: + 81-75-753-3728
- 京都大学理学研究科数学教室 ブノワ・コリンズ
- 075-753-3728