Future Targets in the Classification Program for Amenable C*-Algebras (17w5127)

The Banff International Research Station will host the "Future Targets in the Classification Program for Amenable C*-Algebras" workshop from September 3rd to September 8th, 2017.

C*-algebras are mathematical objects that originally arose in quantum physics. Beyond these origins, C*-algebra theory gained stature as it was quickly realized that C*-algebras can encode key information about other mathematical objects, such as symmetries, networks, large data sets, and time-evolving systems. These constructions follow a common pattern: a mathematical object (such as a group of symmetries) is input and a C*-algebra is output. They suggest an important problem: what do properties of the output C*-algebra tell us about the input mathematical object?

This workshop focuses on a program that systematically answers this question: the classification of C*-algebras. The overarching objective of this program is to identify computable data about C*-algebras, that is sufficiently rich to tell when two differently-constructed C*-algebras are, in fact, the same. This has been a sustained, intensive research project over the last twenty years, and the workshop will take particular advantage of exceptional breakthroughs made in the past years.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides
an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disc
iplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineeri
ng Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional
de Ciencia y Tecnología (CONACYT).