月曜解析セミナー：On the Supports of Levy Processes on Compact Quantum Groups, Uwe Franz 氏

Time：16:30-18:00

Place：理学部3号館3-210室

Organizer：小林 政晴、洞 彰人、長谷部 高広、浜向 直、佐藤 僚亮

Speaker：Uwe Franz 氏 (Universite Marie & Louis Pasteur)

Title：On the Supports of Levy Processes on Compact Quantum Groups

Abstract：In this talk I will give an introduction to the theory of L\’evy processes with values in compact quantum groups. Sch\”urmann’s L\’evy processes on bialgebras or Hopf algebras and Woronowicz’ compact quantum groups are natural noncommutative (or quantum) generalisations of stochastic processes with stationary and independent increments and compact groups. Combining these two theories allows to apply ideas from probability to the study of the noncommutative geometric structure of quantum groups. Using the notion of Gaussian L\’evy processes due to Sch\”urmann, we have given a new definition of the connected component of the identity of a compact quantum group. More generally, we investigate also the smallest closed subgroup which can be reached `continuously’ from a fixed subgroup, which we call its Sch\”urmann envelope. I will present our recent results on these Gaussian parts and Sch\”rmann envelopes, and conclude with several open problems.