一小时邀请报告简介之十九：源于量子力学

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一小时邀请报告简介之十九：源于量子力学
（转自2006年国际数学家大会官方网站）

Plenary Lecture: Sorin Popa
With the roots in quantum mechanics

Like much of today';s mathematics, the subject that professor Sorin Popa will talk about in his plenary lecture, the ``theory of operator algebras';';, is deeply rooted into physics, more precisely quantum mechanics. The study of algebras of operators on Hilbert space began in the 1920';s, in the work of the famous mathematician John von Neumann, in his effort to create a rigurous framework for Heisenberg';s quantum mechanics. The important discovery of Heisenberg (for which he received a Nobel Prize in Physics in 1932) was that observables in particle physics behave like infinite matrices under multiplication, rather than as functions on the phase space, as in classical mechanics. Infinite matrices are nothing but operators on the Hilbert space and von Neumann';s idea was to analyze such operators in the framework of the algebras they generate, which now bare his name ``von Neumann algebras';';.

These algebras were intensely studied over the next several decades, leading to the development of a very powerful, specific kind of analysis. They proved to have a rich and deep structure theory, and owing to mathematicians such as Alain Connes (Fields Medal 1982) and Vaughan Jones (Fields Medal 1990), they became powerful tools in many areas of mathematics, such as ergodic theory, non-commutative geometry/topology, knot theory, statistical mechanics, etc.

Sorin Popa will report on important progress made during the last 6-8 years in this area of research, with the discovery of some totally unexpected ``rigidity phenomena';'; for von Neumann algebras arising from actions of groups  on measure spaces. The results he will present combine functional analysis (operator algebra), ergodic theory and group theory. The fruitful interplay of these subjects is one of the highlights in recent years mathematics.

Sorin Popa graduated in 1977 from the University of Bucharest, where he also got his PhD in 1983. He is a mathematics professor at the University of California Los Angeles (UCLA), a position he held since 1987. He was an invited speaker in section 9 at the ICM in Kyoto, Japan, in 1990, and a main speaker at many conferences in operator algebras, ergodic theory and group theory.

Speaker: Sorin Popa
Title: Deformation and Rigidity for Group Actions and von Neumann Algebras
Date: Saturday, August 26th: 10:15-11:15