On the rigidity of virtual symmetries of II_1 factors

Abstract: One of the most fascinating aspects in the analysis of non-commutative spaces (aka von Neumann algebras), is the way their building data, which is often geometric in nature, impacts on their generalized (or virtual) symmetry picture. This is particularly the case for II_1 factors, where virtual symmetries are encoded by subfactors of finite Jones index, a numerical invariant that can be quantized in intriguing ways. I will discuss some results and open problems that illustrate the unique interplay between analysis and algebra/combinatorics entailed by this interdependence, that's specific to subfactor theory.

operator algebras

Audience: researchers in the topic

Conference on operator algebras and related topics in Istanbul, 2021