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FIELD
Math: HCMC
DATE
Jul 25 (Fri), 2025
TIME
14:30 ~ 15:30
PLACE
1423
SPEAKER
Jeong, Yoonje
HOST
Jung, Mingu
INSTITUTE
서울대학교
TITLE
[HG_AP] Free Probability in Operator Algebras
ABSTRACT
Free probability has proved to be an unexpectedly powerful tool for longstanding questions in operator algebras. In this expository talk, based on the speaker’s personal selection, we will survey three examples that illustrate the theme: • Metric characterisations of freeness: Beginning from Kesten’s result for group von Neumann algebras, we will see how Cadilhac and Collins generalized this result in the setting of free probability, giving a new route to embeddings of free group factors. • Haagerup–Thorbjørnsen’s Strong Convergence Result: We will see how their work for strong convergence of suitable unitary random-matrices was able to solve a problem in operator algebras. • Ultrapowers, free entropy and asymptotic freeness: We discuss how free entropy and asymptotic freeness results can probe the elementary isomorphism problems for II_1 factors.
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