Common trends in Operator Algebra and Number Theory

Abstract: Many years ago (almost 30) Vaughan Jones initiated an approach to a new program of understanding of automorphic forms as Operator Algebra objects. There are naturally associated $II_1$ factors ( in the free groups factors series) His original motivation was to understand if Hecke subgroups could be possibly related to a more natural construction of non-integer index subfactors in free group factors.. There is one "mystery trace vector (s)" which one would like to understand, and this showed up again in his late work. I will discuss these topics and their relations to other problems in number theory that have a natural Operator Algebra counterpart.

operator algebras

Audience: researchers in the topic

Conference on operator algebras and related topics in Istanbul, 2021