BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dmitri Vassiliev (University College London) DTSTART:20200528T090000Z DTEND:20200528T095000Z DTSTAMP:20260416T065024Z UID:IML-SMR/3 DESCRIPTION:Title: Geometric wave propagator on Riemannian manifolds\nby Dmitri Vassiliev (University College London) as part of Scattering\, microlocal analysis a nd renormalisation\n\n\nAbstract\nWe study the propagator of the wave equa tion on a closed Riemannian manifold M. We propose a geometric approach to the construction of the propagator as a single oscillatory integral globa l both in space and in time with a distinguished complex-valued phase func tion. This enables us to provide a global invariant definition of the full symbol of the propagator - a scalar function on the cotangent bundle - an d an algorithm for the explicit calculation of its homogeneous components. The central part of the talk is devoted to the detailed analysis of the s ubprincipal symbol\; in particular\, we derive its explicit small time asy mptotic expansion. We present a general geometric construction that allows one to visualise topological obstructions and describe their circumventio n with the use of a complex-valued phase function. We illustrate the gener al framework with explicit examples in dimension two.\n LOCATION:https://researchseminars.org/talk/IML-SMR/3/ END:VEVENT END:VCALENDAR