程嵩 , 刘锦鹏 , 刘正伟 , 刘子文

刘伟华

2026年10月30日 16:00 至 17:30

Online

Zoom 230 432 7880 (BIMSA)

The isomorphism problem for free group factors has been a central motivation for the development of free probability and the structure theory of von Neumann algebras. This talk surveys its history through the contributions of Dan Voiculescu. We begin with free independence, semicircular and circular systems, and asymptotic freeness of random matrices, explaining how these ideas provide concrete models for free group factors. We then focus on free entropy and free entropy dimension, their role in the search for invariants, and Voiculescu’s landmark proof that free group factors have no Cartan subalgebras. We also introduce his differential approach through free difference quotients, conjugate variables, and liberation, highlighting connections between probabilistic models and operator-algebraic structure. Related contributions of Dykema, Rădulescu, Popa, Ozawa, and others are briefly placed in context.

刘伟华，现任浙江大学百人计划研究员，2016年毕业于加州大学伯克利分校，师从自由概率理论创始人 Dan Voiculescu