Departement Mathematik

Analysis seminar

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For Zoom URL please contact Laura Keller

Herbstsemester 2009

Datum / Zeit Referent:in Titel Ort
22. September 2009
15:15-16:15 		Pierre Germain
Courant Institute, New York University
Details

Analysis Seminar

Titel Global existence for the water wave equation
Referent:in, Affiliation Pierre Germain, Courant Institute, New York University
Datum, Zeit 22. September 2009, 15:15-16:15
Ort HG G 43
Abstract The water wave equation describes the behaviour of the free surface of an ideal (non viscous) fluid. I will first present this equation, and discuss its local well-posedness. Then I will describe a proof of global existence for small, localized, and regular data. This proof relies on a new method, which can be applied to any nonlinear dispersive equation. This is joint work with Nader Masmoudi and Jalal Shatah.
Global existence for the water wave equationread_more
HG G 43
29. September 2009
15:15-16:15 		Prof. Dr. Reza Pakzad
University of Pittsburgh
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Analysis Seminar

Titel Scaling laws and limit models for non-Euclidean Elasticity functionals
Referent:in, Affiliation Prof. Dr. Reza Pakzad, University of Pittsburgh
Datum, Zeit 29. September 2009, 15:15-16:15
Ort HG G 43
Abstract It is well known that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one could seek a deformation yielding the closest metric realization. In this talk, we set up a variational formulation of this problem by introducing a non-Euclidean version of nonlinear elasticity functionals. The corresponding variational problem describes elastic structures and growing tissues (leaves, flowers or marine invertebrates) which exhibit non-zero strain at free equilibria. We discuss the scaling laws and $\Gamma$-limits of the introduced 3d functional on thin plates in the limit of vanishing thickness. One important feature is the study of Sobolev spaces of isometries and infinitesimal isometries. In particular, we obtain an equivalent condition for existence of a W{2,2} isometric immersion of a given 2d metric into R3.
Scaling laws and limit models for non-Euclidean Elasticity functionalsread_more
HG G 43
6. Oktober 2009
15:15-16:15
Details

Analysis Seminar

Titel no seminar
Referent:in, Affiliation
Datum, Zeit 6. Oktober 2009, 15:15-16:15
Ort HG G 43
no seminar
HG G 43
13. Oktober 2009
15:15-16:15
Details

Analysis Seminar

Titel no seminar
Referent:in, Affiliation
Datum, Zeit 13. Oktober 2009, 15:15-16:15
Ort HG G 43
no seminar
HG G 43
20. Oktober 2009
15:15-16:15 		Prof. Dr. Rafe Mazzeo
Department of Mathematics, Stanford University
Details

Analysis Seminar

Titel Ricci flow on open surfaces
Referent:in, Affiliation Prof. Dr. Rafe Mazzeo, Department of Mathematics, Stanford University
Datum, Zeit 20. Oktober 2009, 15:15-16:15
Ort HG G 43
Abstract I will discuss convergence results for the Ricci flow in two dimensions for various classes of complete geometries. The new emphasis is on preservation or change of asymptotic type at spatial infinity.
Ricci flow on open surfacesread_more
HG G 43
27. Oktober 2009
15:15-16:15 		Prof. Dr. Sergei Kuksin
Ecole Polytechnique, Paris
Details

Analysis Seminar

Titel Vey's theorem in infinite dimension and its application to KdV
Referent:in, Affiliation Prof. Dr. Sergei Kuksin, Ecole Polytechnique, Paris
Datum, Zeit 27. Oktober 2009, 15:15-16:15
Ort HG G 43
Vey's theorem in infinite dimension and its application to KdV
HG G 43
3. November 2009
15:15-16:15 		Prof. Dr. Spyros Alexakis
Toronto University
Details

Analysis Seminar

Titel A black hole uniqueness theorem
Referent:in, Affiliation Prof. Dr. Spyros Alexakis, Toronto University
Datum, Zeit 3. November 2009, 15:15-16:15
Ort HG G 43
Abstract I will discuss recent joint work with A. Ionescu and S. Klainerman on the black hole uniqueness problem. A classical result of Hawking (building on earlier work of Carter and Robinson) asserts that any vacuum, stationary black hole exterior region must be isometric to the Kerr exterior, under the restrictive assumption that the space-time metric should be analytic in the entire exterior region. We prove that Hawking's theorem remains valid without the assumption of analyticity, for black hole exteriors which are apriori assumed to be "close" to the Kerr exterior solution in a very precise sense. Our method of proof relies on certain geometric Carleman-type estimates for the wave operator.
A black hole uniqueness theoremread_more
HG G 43
10. November 2009
15:15-16:15 		Prof. Dr. Norbert Hungerbühler
University of Fribourg
Details

Analysis Seminar

Titel Young measures and heat flow problems
Referent:in, Affiliation Prof. Dr. Norbert Hungerbühler, University of Fribourg
Datum, Zeit 10. November 2009, 15:15-16:15
Ort HG G 43
Abstract Let $M$ and $N$ be compact smooth Riemannian manifolds without boundaries. Then, for a map $u:M\to N$ we consider a class ofenergies which includes the the popular Dirichlet energy and the moregeneral $p$-energy. Geometric or physical questions motivate toinvestigate the critical points of such an energy or the correspondingheat flow problem. In the case of the Dirichlet energy, the heat flowproblem has been intensively studied and is well understood by now.However, it has turned out that the case of the $p$-energy ($p\neq2$)is much more difficult in many respects. We give a survey of theknown results for the $p$-harmonic flow and indicate how these resultscan be extended to a larger class of energy types by using Youngmeasure techniques which have been developed for stationary problems in recent years.
Young measures and heat flow problemsread_more
HG G 43
17. November 2009
15:15-16:15
Details

Analysis Seminar

Titel no seminar
Referent:in, Affiliation
Datum, Zeit 17. November 2009, 15:15-16:15
Ort HG G 43
no seminar
HG G 43
24. November 2009
15:15-16:15 		Dr. Ruben Jakob
University of Duisburg-Essen, Germany
Details

Analysis Seminar

Titel Exclusion of boundary branch points of minimal surfaces
Referent:in, Affiliation Dr. Ruben Jakob, University of Duisburg-Essen, Germany
Datum, Zeit 24. November 2009, 15:15-16:15
Ort HG G 43
Unterlagen Abstractfile_download
Exclusion of boundary branch points of minimal surfacesread_more
HG G 43
1. Dezember 2009
15:15-16:15 		Michael Blaser
ETH Zurich, Switzerland
Details

Analysis Seminar

Titel A Minimality property for entropic solutions to scalar conservation laws in 1 + 1 dimensions
Referent:in, Affiliation Michael Blaser, ETH Zurich, Switzerland
Datum, Zeit 1. Dezember 2009, 15:15-16:15
Ort HG G 43
A Minimality property for entropic solutions to scalar conservation laws in 1 + 1 dimensions
HG G 43
8. Dezember 2009
15:15-16:15 		László Székelyhidi
Universität Bonn
Details

Analysis Seminar

Titel Rigidity and flexibility for isometric embeddings in low dimension
Referent:in, Affiliation László Székelyhidi, Universität Bonn
Datum, Zeit 8. Dezember 2009, 15:15-16:15
Ort HG G 43
Abstract A classical theorem in geometry says that the standard 2-sphere is rigid, it is unbendable. On the other hand, the celebrated result of Nash and Kuiper shows that one can nevertheless "crumple" the sphere into an arbitrarily small volume, without creating creases! In more precise terms, whilst there is essentially a unique isometric embedding of the sphere of class C2, there is a huge set of embeddings of class C1. The difference of course lies in the curvature. Borisov proved in the 1950s that the rigidity result can be extended to embeddings with Hölder continuous derivative of order 2/3+, whereas in 1965 he announced that the Nash-Kuiper construction - leading to flexibility- still works with Hölder contiuous derivatives of order 1/7-. In the talk I will revisit these results with a more modern "PDE-approach", based on joint work with Sergio Conti and Camillo De Lellis. At the end of the talk I will comment on the relevance of the latter construction to turbulence.
Rigidity and flexibility for isometric embeddings in low dimensionread_more
HG G 43
15. Dezember 2009
15:15-16:15 		Galina Perelman
Ecole Polytechnique, Paris
Details

Analysis Seminar

Titel Two soliton collision for nonlinear Schrodinger equations in dimension 1
Referent:in, Affiliation Galina Perelman, Ecole Polytechnique, Paris
Datum, Zeit 15. Dezember 2009, 15:15-16:15
Ort HG G 43
Two soliton collision for nonlinear Schrodinger equations in dimension 1
HG G 43

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

Archiv: FS 24 HS 23 FS 23 HS 22 FS 22 HS 21 FS 21 HS 20 FS 20 HS 19 FS 19 HS 18 FS 18 HS 17 FS 17 HS 16 FS 16 HS 15 FS 15 HS 14 FS 14 HS 13 FS 13 HS 12 FS 12 HS 11 FS 11 HS 10 FS 10 HS 09

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