Theme

Representation Theory and its Applications

Theme of my research is representation theory and its applications. We study concrete algebras which appear in Lie theory (one of central objects of study has been cyclotomic Hecke algebras) with various sophisticated techniques.

Let us recall a proverb “Good in theory, the devil is in the detail”. When we apply general theory to a concrete algebra to know something, we often need enormous new ideas to know the answer. Applying general theories such as the theory of Kashiwara crystals, the Auslander-Reiten theory and others, we have found and we will find new ideas and new research topics.

Let me say a few words about my taste in mathematics.

1. I prefer results which have some combinatorial flavor, but I prefer an algebraic proof than a combinatorial proof whenever it is possible.
2. In my opinion, an ideal result is a result which we may state in plain terms but cannot prove without using modern mathematics.

I welcome foreign students who have interest in representation theory. Some basic knowledge on module theory over finite dimensional algebras, cohomology theories, algebraic geometry etc. would be very helpful. If you are interested in my lab, check the Amer. Math. Soc. math.sci.net citations to know my past work. I expect that an applicant has taken basic undergraduate courses in pure mathematics and is familiar with groups, rings and fields at least.

Contact

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