BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Darius Erös (University of Wien) DTSTART:20260521T120000Z DTEND:20260521T133000Z DTSTAMP:20260708T015635Z UID:SissaAnalysisSeminar/14 DESCRIPTION:Title: Singularity structures for nonsmooth spaces\nby Darius E rös (University of Wien) as part of SISSA's Analysis seminars\n\nLecture held in 133.\n\nAbstract\nIn the geometric study of distributions\, the no tions of singular support and wave front set provide essential tools for t he analysis of singularities and their propagation. From an operator-theor etic perspective\, these notions can be captured by studying actions of sm ooth functions and pseudodifferential operators on a given distribution. A bstracting from this point of view\, Dave and Kunzinger have introduced a unifying categorical framework of so-called singularity structures for Fr échet modules\, which recovers the usual notions of singular support and wave front set for closed manifolds.\n\nIn this talk\, we will discuss the ir approach and describe a generalization of their results to the setting of complete (noncompact) manifolds. We will give a refined description of Sobolev regularity in terms of tameness properties of an associated evalua tion map on smoothing operators\, and introduce a substitute for the algeb ra of pseudodifferential operators. Our construction is based entirely on the functional calculus of the Laplacian\, with the aim of applying these techniques in the study of (infinitesimally Hilbertian) metric measure spa ces.\nThis is based on ongoing work with Günther Hörmann and Michael Kun zinger.\n LOCATION:https://researchseminars.org/talk/SissaAnalysisSeminar/14/ END:VEVENT END:VCALENDAR