Speaker: 刘伟华 (浙江大学)
Time: 2026-03-05 14:30-15:30
Location: 1010, SIMIS
Abstract:
Firstly, we will introduce the notion of free independence, which comes from Voiculescu’s probabilistic method to attack the free group von Neumann algebra isomorphism problem. Then, we introduce free analogues of certain classical groups, which are compact quantum groups in the sense of Woronowicz. There is a canonical way to define symmetric invariants on operator algebras with faithful states from compact quantum groups. With those symmetric conditions, we are able to determine the relations between generators of given von Neumann algebras conditionally by Kostler, Speicher, Curran, etc. These results are called de Finetti type theorems. In my recent work, we will provide a full classification of de Finetti type theorems for non-selfadjoint generators in both the commutative and free case. If time permits, we will explain the possible symmetries between classical and free case.
About Speaker:
Liu Weihua is currently a Hundred Talents Program Professor at Zhejiang University. He joined Zhejiang University in 2020 and was selected for the National Overseas High-level Young Talents Program. His current research primarily focuses on von Neumann algebras, free probability theory, random matrices, quantum groups, and quantum measurement theory. He has published numerous articles in journals such as Advances in Mathematics, Communications in Mathematical Physics, Journal of Functional Analysis, and Transactions of the American Mathematical Society. In 2014, he was awarded the Birkhoff-von Neumann Prize by the International Quantum Structures Association.
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