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.


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

qr code