SCIENTIFIC ACTIVITIES

August 21, 2014

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th ANNIVERSARY YEAR

Back2Fields COLLOQUIUM SERIES
September 13, 2012 at 4:30p.m.
Fields Institute, (map)


Andrew Toms
Purdue University
Tensorial absorption and the structure of operator algebras
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The theory of rings of bounded operators on Hilbert space was initiated by Murray and von Neumann in the 1930s, and has since developed in myriad directions. Among these we single out the theory of noncommutative topological spaces (C*-algebras) and noncommutative measure spaces (von Neumann algebras), and examine the structure of those objects which can reasonably be called amenable. Here we find a common theme: deep information about the structure of these algebras is often rooted in their tensorial absroption of a canonical tractable algebra. For II_1 factors this object is the hyperfinite II_1 factor, and for purely infinite nuclear C*-algebras it is the Cuntz algebra O_\infty. For general nuclear simple separable C*-algebras, the correct object is the Jiang-Su algebra Z. In this talk we will discuss progress on proving tensorial absorption of Z, and its consequences for the classification theory of C*-algebras.


The Back2Fields Colloquium Series celebrates the accomplishments of former postdoctoral fellows of Fields Institute thematic programs. Over the past two decades, these programs attracted the rising stars of their field and often launches very distinguished research careers. As part of the 20th anniversary celebrations, this series of colloquium talks will allow the general mathematical public to become familiar with some of their work.




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