BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Punya Satpathy (U. Michigan) DTSTART:20210330T150000Z DTEND:20210330T160000Z DTSTAMP:20260423T024447Z UID:GNTRT/9 DESCRIPTION:Title: Sc attering theory on Locally Symmetric Spaces\nby Punya Satpathy (U. Mic higan) as part of Geometry\, Number Theory and Representation Theory Semin ar\n\n\nAbstract\nIn 1976\, Victor Guillemin published a paper discussing geometric scattering theory\, in which he related the Lax-Phillips Scatter ing matrices (associated to a noncompact hyperbolic surface with cusps) an d the sojourn times associated to a set of geodesics which run to infinity in either direction.\nLater\, the work of Guillemin was generalized to lo cally symmetric spaces by Lizhen Ji and Maciej Zworski. In the case of a $ \\Q$-rank one locally symmetric space $\\Gamma \\backslash X$\, they const ructed a class of scattering geodesics which move to infinity in both dire ctions and are distance minimizing near both infinities. An associated soj ourn time was defined for such a scattering geodesic\, which is the time it spends in a fixed compact region. One of their main results was that th e frequencies of oscillation coming from the singularities of the Fourier transforms of scattering matrices on $\\Gamma \\backslash X$ occur at sojo urn times of scattering geodesics on the locally symmetric space. \n\nIn t his talk I will review the work of Guillemin\, Ji and Zworski as well as d iscuss the work from my doctoral dissertation on analogous results for hig her rank locally symmetric spaces. In particular\, I will describe higher dimensional analogues of scattering geodesics called $\\textbf{Scattering Flat}$ and study these flats in the case of the locally symmetric space gi ven by the quotient\n$SL(3\,\\mathbb{Z}) \\backslash SL(3\,\\mathbb{R}) / SO(3)$. A parametrization space is discussed for such scattering flats as well as an associated vector valued parameter (bearing similarities to soj ourn times) called $\\textbf{sojourn vector}$ and these are related to the frequency of oscillations of the associated scattering matrices coming fr om the minimal parabolic subgroups of $\\text{SL}(3\,\\mathbb{R})$. The ke y technique is the factorization of higher rank scattering matrices.\n LOCATION:https://researchseminars.org/talk/GNTRT/9/ END:VEVENT END:VCALENDAR