BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Thomas Gotfredsen DTSTART:20200804T130000Z DTEND:20200804T140000Z DTSTAMP:20260423T035717Z UID:GOBA/4 DESCRIPTION:Title: The quantised interval as a quantum metric space\nby Thomas Gotfredsen as part of Groups\, Operators\, and Banach Algebras Webinar\n\n\nAbstract\nT he study of metrics on state spaces arising from semi-norms dates back to Connes and was formalised as the notion of a compact quantum metric space by Rieffel\, whose notion of quantum Gromov-Hausdorff distance on the clas s of compact quantum metric spaces\, has established a new famework for th e study of approximations of C*-algebras. \n\nIn a recent paper\, Aguilar and Kaad have shown that the standard Podleś sphere\, originally introduc ed as the homogeneous space for Woronowicz' quantum SU(2)\, is in fact a c ompact quantum metric space\, and they posed the rather natural question\, whether the standard Podleś sphere converges to the standard 2-sphere in the quantum analogues of the Gromov-Hausdorff distance as the deformation parameter tends to 1 . \nIn my talk based on joint work with Jens Kaad an d David Kyed\, I will present some new developments to the above question. In particular we have shown that the commutative C*-subalgebras generated by the self-adjoint generator of the standard Podleś sphere\, converge t o the interval of length \\pi as one would expect if the more general conv ergence result is true\, and that the spaces in fact vary continuously. Th is provides some evidence that the convergence result for the Podles spher es may hold true as well (this is currently work in progress).\n LOCATION:https://researchseminars.org/talk/GOBA/4/ END:VEVENT END:VCALENDAR