NSF/CBMS Regional Conference in the Mathematical Sciences

Topological and algebraic regularity properties of nuclear C*-algebras

May 11-15, 2012

University of Louisiana at Lafayette

Principal Speaker: Wilhelm Winter (Muenster)
Invited Speakers: Ilijas Farah (York), David Kerr (Texas A&M), Ian Putnam (Victoria)
Organizers: Gary Birkenmeier (UL - Lafayette), Nate Brown (Penn State), Daniel Davis (UL - Lafayette), Thierry Giordano (Ottawa), P. W. Ng (UL - Lafayette), Leonel Robert (UL - Lafayette)

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Wilhelm Winter


There are several notions of "topological dimension" for noncommutative C*-algebras, each with their own strengths. Recent work of Wilhelm Winter and collaborators has resulted in a new "nuclear" dimension that is very natural, generalizes classical covering dimension of spaces, and is known to be finite (in fact, < 6) for all simple, nuclear C*-algebras that have been classified so far. This work is inspired by classification, but has led to substantial insights into the structure of arbitrary nuclear C*-algebras (i.e., inspired by said work, Kirchberg has proved they enjoy a stronger approximation property than was previously known) and a new definition of "Rokhlin dimension" for homeomorphisms of compact spaces which is purely topological and extends the classical Rokhlin property (which is the zero-dimensional case).

Given the history of applications of operator algebras to dynamics, from Connes-Feldman-Weiss to Popa's groundbreaking work on the W*-side and Giordano-Putnam-Skau and related results on the C*-side, the above breakthroughs are particularly exciting.

The lectures are designed to be very accessible to graduate students with limited backgrounds and to mathematicians who know only the basics of C*-algebra theory. Open problems and new research opportunities for beginning researchers and students will be discussed.


Notes taken by Stuart White during the lectures (not proof read!).

Lecture 1: Introduction and motivation
Lecture 2: Topological dimension
Lecture 3: Strongly self-absorbing C*-algebras
Lecture 4: The Jiang--Su algebra
Lecture 5: Z-stable classification
Lecture 6: The Cuntz semigroup and perfect C*-algebras
Lecture 7: Decomposition rank, perfectness and Z-stability
Lecture 8: Minimal dynamical systems
Lecture 9: Dynamics and dimension
Lecture 10: Outlook. Open problems

UPDATES: Titles and abstracts, Group photo.
The conference is committed to the strengthening and enrichment of the mathematics personnel base and development of the local region. Students, junior mathematicians, mathematicians from underrepresented groups and researchers from the local region are encouraged to apply for support.

Please send any questions to cbms2012@louisiana.edu or to any of the organizers.