Von Neumann Algebras in the 21st Century

报告题目:Von Neumann Algebras in the 21st Century


报告人:Mingchu Gao, Professor of Mathematics, Louisiana College, Pineville, LA






摘要:We will give an overview of several historical achievements in the history of von Neumann algebras. (1) Two basic constructions of von Neumann algebras given by Murray and von Neumann in 1940's: group von Neumann algebras, and group measure space constructions. (2) Connes classi_cation results on amenable von Neumann algebras in 1970's. (3) Voiculescu's free probability theory in 1980's-1990's: (i) Professor Liming Ge's work (ii) Ozawa's work (iii) the work of Junge and Gao. (4) Popa's deformation, rigidity, and intertwining theory in the 21st century: (i) Basic theory (ii) Applications to Kadison's fundamental group problem (iii) Applications to the classi_cation of Murray-von Neumann's group measure space constructions.




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