Analysis seminar

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For Zoom URL please contact Laura Keller

Autumn Semester 2011

Date / Time Speaker Title Location
20 September 2011
15:15-16:15
Prof. Dr. Esther Cabezas-Rivas
Universität Münster, Germany
Event Details

Analysis Seminar

Title How to produce a Ricci Flow via Cheeger-Gromoll exhaustion.
Speaker, Affiliation Prof. Dr. Esther Cabezas-Rivas, Universität Münster, Germany
Date, Time 20 September 2011, 15:15-16:15
Location HG G 43
Abstract We will talk about how to prove short time existence for the Ricci flow on open manifolds of nonnegative complex sectional curvature. We do not require upper curvature bounds. By considering the doubling of convex sets contained in a Cheeger-Gromoll convex exhaustion and solving the singular initial value problem for the Ricci flow on these closed manifolds, we obtain a sequence of closed solutions of the Ricci flow with nonnegative complex sectional curvature which subconverge to a solution of the Ricci flow on the open manifold. Furthermore, we find an optimal volume growth condition which guarantees long time existence, and we give an analysis of the long time behaviour of the Ricci flow. Finally, we construct an explicit example of an immortal nonnegatively curved solution of the Ricci flow with unbounded curvature for all time.
How to produce a Ricci Flow via Cheeger-Gromoll exhaustion.read_more
HG G 43
27 September 2011
15:15-16:15
Maciej Zworski
University of California, Berkeley
Event Details

Analysis Seminar

Title Control for Schroedinger operators on tori
Speaker, Affiliation Maciej Zworski, University of California, Berkeley
Date, Time 27 September 2011, 15:15-16:15
Location HG G 43
Abstract A well known result of Jaffard states that an arbitrary region on a torus controls, in the L2 sense, solutions of the free stationary and dynamical Schroedinger equations. In this note we show that the same result is valid in the presence of a potential, that is for Schroedinger operators with continuous potentials.
Control for Schroedinger operators on toriread_more
HG G 43
4 October 2011
15:15-16:15
Andrea Mondino
SISSA, Italy
Event Details

Analysis Seminar

Title The Willmore and others L^2 curvature functionals in Riemannian manifolds
Speaker, Affiliation Andrea Mondino, SISSA, Italy
Date, Time 4 October 2011, 15:15-16:15
Location HG G 43
Abstract Given an immersion $f$ of a surface $\Sigma$ into $\R^3$, called $H$ the mean curvature of the immersion, the Willmore functional is defined as the $L^2$ norm of the mean curvature up to a factor: W(f):=\frac{1}{4}\int H^2. If we consider immersions in a Riemannian manifold $(M,g)$ there are many possible generalizations of the Willmore functional $W$; in the seminar we will speak about these generalizations and study the existence of minimizers and critical points of the corresponding functionals under curvature conditions on the ambient manifold $(M,g)$. The topic has links with general relativity, string theory, biology, nonlinear elasticity theory etc.
The Willmore and others L^2 curvature functionals in Riemannian manifoldsread_more
HG G 43
11 October 2011
15:15-16:15
Christina Sormani

Event Details

Analysis Seminar

Title Near Equality in the Riemannian Positive Mass Theorem and the Penrose Inequality
Speaker, Affiliation Christina Sormani,
Date, Time 11 October 2011, 15:15-16:15
Location HG G 43
Abstract The Schoen-Yau Positive Mass Theorem states that an asymptotically flat 3 manifold with nonnegative scalar curvature has positive ADM mass unless the manifold is Euclidean space. Here we examine sequences of such manifolds whose ADM mass is approaching 0. We assume the sequences have no interior minimal surfaces although we do allow them to have boundary if it is a minimal surface as is assumed in the Penrose inequality. We conjecture that they converge to Euclidean space in the pointed Intrinsic Flat sense for a well chosen sequence of points. The Intrinsic Flat Distance, introduced in work with Stefan Wenger (UIC), can be estimated using filling manifolds which allow one to control thin wells and small holes. Here we present joint work with Dan Lee (CUNY) constructing such filling manifolds explicitly and proving the conjecture in the rotationally symmetric case.
Near Equality in the Riemannian Positive Mass Theorem and the Penrose Inequalityread_more
HG G 43
25 October 2011
15:15-16:15
Dr. Melanie Rupflin
MPI Potsdam/Golm
Event Details

Analysis Seminar

Title Flowing maps to minimal surfaces
Speaker, Affiliation Dr. Melanie Rupflin, MPI Potsdam/Golm
Date, Time 25 October 2011, 15:15-16:15
Location HG G 43
Abstract We introduce a new flow for maps from compact surfaces of arbitrary genus to general Riemannian manifolds that has elements in common with the harmonic map flow and also with the mean curvature flow and explain how it may be used to find minimal immersions. The presented results are joint work with Peter Topping.
Flowing maps to minimal surfacesread_more
HG G 43
25 October 2011
16:30-17:30
Dr. Gilbert Weinstein
Monash University, Australia
Event Details

Analysis Seminar

Title On Riemannian Penrose inequalities with charge
Speaker, Affiliation Dr. Gilbert Weinstein, Monash University, Australia
Date, Time 25 October 2011, 16:30-17:30
Location HG G 43
Abstract The Riemannian Penrose inequality states that the total mass of an asymptotically flat 3-manifold with non-negative scalar curvature is not less than half the area radius of the outermost horizon with equality only in the case of the Schwarzschild metric. Several natural generalizations to the charged case can be proposed. We present counter-examples to some of these generalizations and discuss a tentative approach to prove the remaining one.
On Riemannian Penrose inequalities with chargeread_more
HG G 43
22 November 2011
15:15-16:15
Prof. Dr. Hakan Eliasson
Paris 7
Event Details

Analysis Seminar

Title "The Birkhoff normal form and a problem of M. Herman"
Speaker, Affiliation Prof. Dr. Hakan Eliasson, Paris 7
Date, Time 22 November 2011, 15:15-16:15
Location HG G 43
Assets AbstractEliassonfile_download
"The Birkhoff normal form and a problem of M. Herman"read_more
HG G 43
6 December 2011
15:15-16:15
Prof. Dr. Herbert Koch
University of Bonn
Event Details

Analysis Seminar

Title Selfsimilar blow up for the supercritical generalized Korteweg de Vries equation
Speaker, Affiliation Prof. Dr. Herbert Koch, University of Bonn
Date, Time 6 December 2011, 15:15-16:15
Location HG G 43
Abstract Wave collapse for the cubic focusing nonlinear Schrödinger equation in three space dimensions is the most prominent example of blow-up for supercritical dispersive equations. Despite a fairly detailed heuristic and numerical picture of the blow up analytic progress on the mechanism is recent and fairly limited. I report on the construction of selfsimilar solutions of finite energy to the generalized KdV equation in the slightly super critical regime. Heuristically the self similar solutions are expected to bifurcate from the ground state in the critical case, the exponent being the bifurcation parameter. This turns out to be correct, but the details were unexpected and intricate. Numerical simulations confirm and extend the analytic results.
Selfsimilar blow up for the supercritical generalized Korteweg de Vries equationread_more
HG G 43
13 December 2011
15:15-17:15
Prof. Dr. Simon Brendle
University of Stanford, USA
Event Details

Analysis Seminar

Title Rigidity Questions Involving Scalar Curvature
Speaker, Affiliation Prof. Dr. Simon Brendle, University of Stanford, USA
Date, Time 13 December 2011, 15:15-17:15
Location HG G 43
Rigidity Questions Involving Scalar Curvature
HG G 43

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Organizers: Francesca Da Lio, Tom Ilmanen, Thomas Kappeler, Tristan Rivière, Michael Struwe

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