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For Zoom URL please contact Laura Keller

Spring Semester 2015

Date / Time Speaker Title Location
3 March 2015
15:15-16:15 		Dr. Romain Petrides
ENS Lyon
Event Details

Analysis Seminar

Title Maximal metrics for the Laplace eigenvalues on surface
Speaker, Affiliation Dr. Romain Petrides, ENS Lyon
Date, Time 3 March 2015, 15:15-16:15
Location HG G 43
Abstract Given a compact surface, we deal with an old question (since the works by Yang and Yau in the 80s) about the sequence of the eigenvalues of the Laplacian : Is there some regular Riemannian metric which maximises the k-th eigenvalue on this surface ? We also give the link between this problem and minimal immersions into spheres.
Maximal metrics for the Laplace eigenvalues on surfaceread_more
HG G 43
17 March 2015
15:15-16:15 		Prof. Dr. Reza Pakzad
University of Pittsburgh
Event Details

Analysis Seminar

Title Rigidity and flexibility for the Monge-Ampère equation
Speaker, Affiliation Prof. Dr. Reza Pakzad, University of Pittsburgh
Date, Time 17 March 2015, 15:15-16:15
Location HG G 43
Abstract In this talk, we will explore rigidity and flexibility of the weak type solutions to the Monge-Amp\`ere equation, by replacing the Hessian determinant by other weaker variants, and without any a priori convexity assumptions. Some past and recent results concerning rigid behavior (e.g. convexity or developabilty) of Sobolev solutions in two and higher dimensions will be discussed, while, in contrast, and following convex integration methods \`a la Nash and Kuiper, we show that fixing the so called very weak Hessian determinant as any regular enough distribution, the $C^1$ solutions are dense in the space of all continuous functions (and hence they cannot manifest the same rigidity as the stronger solutions). We will also discuss the rigidity and flexibility of solutions with H\"older continuous derivatives and connections with isometric immersion problem. The talk will be based on joint works with Bob Jerrard (U. of Tornoto) and with M. Lewicka (U. of Pittsburgh).
Rigidity and flexibility for the Monge-Ampère equationread_more
HG G 43
31 March 2015
15:15-16:15 		Prof. Dr. Jeremie Szeftel
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie
Event Details

Analysis Seminar

Title The resolution of the bounded L2 curvature conjecture in general relativity
Speaker, Affiliation Prof. Dr. Jeremie Szeftel, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie
Date, Time 31 March 2015, 15:15-16:15
Location HG G 43
Abstract In order to control locally a space-time which satisfies the Einstein equations, what are the minimal assumptions one should make on its curvature tensor? The bounded $L^2$ curvature conjecture roughly asserts that one should only need $L^2$ bounds of the curvature tensor on a given space-like hypersurface. This conjecture has its roots in the remarkable developments of the last twenty years centered around the issue of optimal well-posedness for nonlinear wave equations. In this context, a corresponding conjecture for nonlinear wave equations cannot hold, unless the nonlinearity has a very special nonlinear structure. I will present the proof of this conjecture, which sheds light on the specific null structure of the Einstein equations. This lecture will require no specific background.
The resolution of the bounded L2 curvature conjecture in general relativityread_more
HG G 43
21 April 2015
15:15-16:15 		Dr. Isabella Ianni
University of Naple
Event Details

Analysis Seminar

Title Asymptotic analysis and sign-changing bubble towers for Lane-Emden problems
Speaker, Affiliation Dr. Isabella Ianni, University of Naple
Date, Time 21 April 2015, 15:15-16:15
Location HG G 43
Abstract We analyze the asymptotic behavior of solutions of the semilinear Lane-Emden problem in smooth bounded 2-dimensional domains when the exponent p of the nonlinearity tends to infinity. In the case of positive solutions we can give a complete description, while for sign-changing solutions the analysis turns out to be more delicate. In particular we show that under suitable symmetry assumptions, the positive and negative parts of families of symmetric solutions concentrate at the same point, and that the limit profile looks like a tower of two different bubbles given by the superposition of a regular and a singular solution of the Liouville problem in the plane. The results are obtained in collaboration with F. De Marchis (Roma Tor Vergata) and F. Pacella (Roma Sapienza).
Asymptotic analysis and sign-changing bubble towers for Lane-Emden problemsread_more
HG G 43
5 May 2015
15:15-16:15 		Prof. Dr. Jan Kristensen
University of Oxford
Event Details

Analysis Seminar

Title The Morse-Sard theorem, generalized Luzin property and level sets for Sobolev functions
Speaker, Affiliation Prof. Dr. Jan Kristensen, University of Oxford
Date, Time 5 May 2015, 15:15-16:15
Location HG G 43
Abstract Many classical results from multivariate calculus can be generalized to suitable Sobolev functions that need not even be everywhere differentiable. In this talk we discuss some new results that have been obtained in joint work with Jean Bourgain (Princeton) and Mikhail Korobkov (Novosibirsk).
The Morse-Sard theorem, generalized Luzin property and level sets for Sobolev functions read_more
HG G 43
12 May 2015
15:15-16:15 		Prof. Dr. Herbert Koch
University of Bonn
Event Details

Analysis Seminar

Title Partial analyticity of solutions to elliptic equations and analyticity of level sets
Speaker, Affiliation Prof. Dr. Herbert Koch, University of Bonn
Date, Time 12 May 2015, 15:15-16:15
Location HG G 43
Abstract I will report on joint work with Nadirashvili on analyticity of level sets of solutions to elliptic equations. It implies analyticity of flow lines of stationary Euler flows in two space dimensions provided the velocity vector field is measurable, bounded, and has one component with a positive lower bound.
Partial analyticity of solutions to elliptic equations and analyticity of level setsread_more
HG G 43
19 May 2015
15:15-16:15 		Prof. Dr. Remi Carles
University of Montpellier
Event Details

Analysis Seminar

Title On semiclassical limit of nonlinear quantum scattering
Speaker, Affiliation Prof. Dr. Remi Carles, University of Montpellier
Date, Time 19 May 2015, 15:15-16:15
Location HG G 43
Abstract We consider the cubic Schrödinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a complete scattering theory is available, showing that both the potential and the nonlinearity are asymptotically negligible for large time. Then, for data under the form of coherent state, we show that a scattering theory is also available for the approximate envelope of the propagated coherent state, which is given by a nonlinear equation. In the semi-classical limit, these two scattering operators can be compared in terms of classical scattering theory, thanks to a uniform in time error estimate. We infer a large time decoupling phenomenon in the case of finitely many initial coherent states.
On semiclassical limit of nonlinear quantum scatteringread_more
HG G 43
26 May 2015
15:15-16:15 		Antonio Lerario
University de Lyon
Event Details

Analysis Seminar

Title Topology of nonholonomic loop spaces
Speaker, Affiliation Antonio Lerario, University de Lyon
Date, Time 26 May 2015, 15:15-16:15
Location HG G 43
Abstract Given two points on a sub-Riemannian manifold the nonholonomic path-space consists of all Lipschitz continuous horizontal curves joining them. The sub-Riemannian structure allows to define the energy of these curves (a function on the nonholomonic path space) and geodesics are critical points of this function. I will discuss some quantitative aspects of this picture both on the infinitesimal scale (on Carnot groups), on the local scale (using a blow-up procedure) and the global scale (generalizing a theorem of Serre).
Topology of nonholonomic loop spacesread_more
HG G 43

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

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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