Conference: CBMS Conference: Classifying Amenable Operator Algebras

The Department of Mathematics of Texas Christian University will host an NSF/CBMS (Conference Board of the Mathematical Sciences) Regional Conference in the Mathematical Sciences titled "Classifying amenable operator algebras", which will take place on its campus in Fort Worth, Texas, from June 9, 2025 to June 13, 2025. The principal lecturer will be Christopher Schafhauser from the University of Nebraska-Lincoln.

The meeting will serve to train working mathematicians and graduate students alike in recent developments and new techniques that have allowed progress in the field of Operator Algebras and their classification. In addition to Professor Schafhauser's main lectures there will be five complementary follow-up talks by additional speakers. The program will also include other activities designed to broaden participation and to provide young researchers in the field opportunities to build professional networks and share their research.

In more detail, operator algebras, including C*-algebras and von Neumann algebras, originally arose from quantum physics. Enduring interest in them is largely due to the realization that they can be constructed from, and in some cases encode, many other structures, such as symmetries, time-evolving systems, graphs, and number fields. Alain Connes' work on the structure and classification of amenable von Neumann algebras in the 1970s remains fundamental to modern von Neumann algebra theory.

In the topological setting of C*-algebras, the classification program for amenable C*-algebras was initiated in the 1990s, seeking analogous results. This large-scale worldwide endeavor recently culminated in the proof of the main conjecture in the area, giving a complete classification of a broad class of simple amenable C*-algebras. This main lectures will provide an accessible introduction to the classification result and the follow-up talks will focus on applications.

The conference will also feature a panel discussion about future research directions. The conference website may be found at https://faculty.tcu.edu/jcarrion/CBMS-2025.html.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.