BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Martijn Caspers (TU Delft\, Netherlands) DTSTART:20201207T150000Z DTEND:20201207T160000Z DTSTAMP:20260404T145132Z UID:QGS/5 DESCRIPTION:Title: Riesz transforms on compact quantum groups and strong solidity\nby Martijn Caspers (TU Delft\, Netherlands) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nThe Riesz transform is one of the most important and classical examples of a Fourier multiplier on the real numbers. It may be described as the operator $\\nabla_j \\Delta^{-1/2}$ where $\\nabla_j = d /dx_j$ is the derivative and $\\Delta$ is the Laplace operator. In a more general context the Riesz transform may always be defined for any diffusio n semigroup on the reals. In case the generator of this semi-group is the Laplace operator the classical Riesz transform is retrieved. In quantum pr obability the quantum Markov semi-groups play the role of the diffusion se mi-groups and again a suitable notion of Riesz transform can be described. \n\nWe show that the Riesz transform may be used to prove rigidity propert ies of von Neumann algebras. We focus in particular on examples from compa ct quantum groups. Using these tools we show that a class of quantum group s admits rigidity properties. The class has the following properties:\n\n( 1) $\\text{SU}_q(2)$ is contained in it.\n\n(2) The class is stable under monoidal equivalence\, free products\, dual quantum subgroups and wreath p roducts with $S^+_N$.\n\nThe rigidity properties include the Akemann-Ostra nd property and strong solidity. Part of this talk is based on joint work with Mateusz Wasilewski and Yusuke Isono.\n LOCATION:https://stable.researchseminars.org/talk/QGS/5/ END:VEVENT END:VCALENDAR