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Home , Gerhard Huisken

University of Oregon Department of

May 23rd – May 25th

Gerhard Huisken

Max Planck Institute of Gravitational Physics (Albert Einstein Institute) In Postdam

LECTURE 1 A tea will precede lectures at 3:30 p.m LECTURE 3 Wednesday, May 23rd, 4pm & Friday, May 25th, 4pm 221 McKenzie A reception will follow 205 Deady the Wednesday lecture “The and in 219 Fenton Hall “Isoperimetric uniformisation in inequalities via Geometric geometry” evolution equations” LECTURE 2 Abstract: th Abstract: Geometric versions of the heat Thursday, May 24 , 4pm To prove isoperimetric equation can be used to deform a 204 Villard inequalities, one strategy given geometrical object into a consists in sweeping out a given "nicer" or even canonical “Isoperimetric inequalities bounded region by a family of representative inside a certain hypersurfaces class. Examples for this and the concept of mass controlled by a suitable geometric phenomenon are Hamilton's flow of in ” evolution equation. The lecture Riemannian metrics by their Ricci explains how the flow of a and the surface in direction of its mean Abstract: flow of hypersurfaces. Recently the curvature vector discussed in the Isoperimetric inequalities have a long reach of these deformations has first lecture can be used in history in Geometry and Analysis, been greatly enhanced by conjunction with inverse mean motivating conceptual progress in these controlling and extending them curvature flowto control areas of mathematics for many centuries. beyond singularities. The lecture isoperimetric properties of an They also paved the way to the explains recent work by Huisken enclosed region. Such understanding of many related variational and Sinestrari on surgery in mean inequalities then justify the problems in . The curvature flow and explains the concept of mass introduced in lecture describes modern analytical relation to the work of Hamilton and the previous lecture. approaches to the age old isoperimetric Perelman on the . problem and explains how a deviation from the standard isoperimetric inequality in curved spaces can be used to develop a natural new concept for the mass of isolated gravitating systems such as stars and black holes in General Relativity.