Speaker: Dr. Glen Wheeler (Wollongong) https://sites.google.com/site/glenwheelermathman/ Time: **Tuesday**, May 28, 12NOON--1PM Room: Carslaw 707A Lunch: after the talk. The reservation at Law Annex Cafe is at 1:10PM. ---------------------------------------------- Title: The Willmore Flow in Riemannian Spaces Abstract: in this talk I will detail recent developments on the Willmore flow of surfaces in 3-manifolds with a prescribed Riemannian structure. If this structure is flat then local parabolic regularity for data in terms of the local L^2-norm of the second fundamental form is contained in Kuwert and Schaetzle’s previous work on the Willmore functional. If there is some ambient curvature then several problems arise: the evolution of key geometric quantities becomes more complex and tools such as the Sobolev inequality are either invalid or hold only in special circumstances. Using a new concentration of area method we are able to recover an analogue of Kuwert and Schaetzle’s local parabolic regularity theorem. We present one application yielding a global existence result in certain ambient spaces. This is joint work with Jan Metzger and Valentina-Mira Wheeler. ---------------------------------------------- Seminar website: http://www.maths.usyd.edu.au/u/SemConf/Geometry/