Operator Algebras, the Renormalization Group, and Jones’ Actions of Thompson’s Groups

Alexander Stottmeister (ITP Hannover)

Jul 19. 2023, 10:00 — 10:45

In many-body quantum physics, the general renormalization group of Kadanoff and Wilson is a fundamental concept used to study the behavior of physical systems under changes of the observational scale. Fixed points of the renormalization group play a distinguished role, leading to a unified understanding of scaling limits and phase transitions as well as universality phenomena. Such fixed points are understood as scale-invariant systems, which possess a particularly large group of symmetries: the conformal group of the underlying physical space. In two-dimensional systems, the conformal group is related to orientation-preserving diffeomorphisms of the unit interval or the circle. Thompson's groups can be understood as a subgroup of piecewise linear approximations of these diffeomorphisms. Following a proposal by Jones to exploit this idea in the construction of models of said fixed points, I will discuss some relatively recent work together with Arnaud Brothier and Tobias J. Osborne in this context.

Further Information
ESI Schrödinger and Boltzmann Lecture Hall
Associated Event:
Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics (Workshop)
Christopher Cashen (U of Vienna)
Javier de la Nuez González (KIAS, Seoul)
Alexandra Edletzberger (U of Vienna)
Yash Lodha (U of Hawaii, Honolulu)