## Geometry Seminar - Abstracts

### Talk

21 March 2016, 16:00 - 17:00, in HG00.310

**Makato Yamashita**
(Ochanomizu University)

*Random walk on monoidal categories and classification of
compact quantum groups*

### Abstract

Motivated by Izumi's noncommutative Poisson boundary for
discrete quantum groups, we define the notion of categorical Poisson
boundary for C*-tensor categories with duality and irreducible unit.
Motivated by subfactor theory we show that this construction has a
universality property for the amenable tensor functors. As an
application, we obtain a classification result which implies that any
compact quantum group with noninvolutive antipode and the same
combinatorial data of representations as SU(n) essentially arises as a
strict quantization for a Poisson-Lie group structure on SU(n).

This
talk is based on joint work with S. Neshveyev.

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