BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:João Pimentel Nunes (Instituto Superior Técnico) DTSTART:20221122T160000Z DTEND:20221122T170000Z DTSTAMP:20260423T022627Z UID:Geolis/96 DESCRIPTION:Title: The geometric interpretation of the Peter-Weyl theorem\nby João Pimen tel Nunes (Instituto Superior Técnico) as part of Geometria em Lisboa (IS T)\n\n\nAbstract\nLet $K$ be a compact Lie group. I will review the constr uction of Mabuchi geodesic families of $K\\times K-$invariant Kahler struc tures on $T^*K$\, via Hamiltonian flows in imaginary time generated by a s trictly convex invariant function on $Lie \\\, K$\, and the corresponding geometric quantization. At infinite geodesic time\, one obtains a rich mix ed polarization of $T^*K$\, the Kirwin-Wu polarization\, which is then con tinuously connected to the vertical polarization of $T^*K$. The geometric quantization of $T^*K$ along this family of polarizations is described by a generalized coherent state transform that\, as geodesic time goes to inf inity\, describes the convergence of holomorphic sections to distributiona l sections supported on Bohr-Sommerfeld cycles. These are in correspondenc e with coadjoint orbits $O_{\\lambda+\\rho}$. One then obtains a concrete (quantum) geometric interpretation of the Peter-Weyl theorem\, where terms in the non-abelian Fourier series are directly related to geometric cycle s in $T^*K$. The role of a singular torus action in this construction will also be emphasized. This is joint work with T.Baier\, J. Hilgert\, O. Kay a and J. Mourão.\n LOCATION:https://researchseminars.org/talk/Geolis/96/ END:VEVENT END:VCALENDAR