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Spring Semester 2013

Date / Time Speaker Title Location
5 March 2013
15:15-16:15 		Lukas Parapatits
University of Vienna of Technology
Event Details

Analysis Seminar

Title On the Structure Theory of Translation Invariant Valuations
Speaker, Affiliation Lukas Parapatits, University of Vienna of Technology
Date, Time 5 March 2013, 15:15-16:15
Location HG G 43
Abstract A valuation is an additive map on convex bodies. The classical examples are volume, surface area and Euler characteristic or any Borel measure restricted to convex bodies. The talk will review some well known results on the structure of the space of valuations, including Hadwiger's classification of continuous rigid motion invariant valuations and McMullen's decomposition of the space of continuous translation invariant valuations. Furthermore, it is possible to embed the subspace of even homogeneous continuous translation invariant valuations into the space of continuous functions on a Grassmannian. This embedding is called the Klain map. I will talk about properties of this embedding and present new results on the inverse Klain map, which have applications to Brunn-Minkowski-type inequalities (joint work with F. E. Schuster and T. Wannerer).
On the Structure Theory of Translation Invariant Valuations read_more
HG G 43
12 March 2013
15:15-16:15 		Dr. Julien Cortier
IHÉS
Event Details

Analysis Seminar

Title On the mass of asymptotically hyperbolic manifolds
Speaker, Affiliation Dr. Julien Cortier, IHÉS
Date, Time 12 March 2013, 15:15-16:15
Location HG G 43
Abstract Asymptotically hyperbolic manifolds arise in a number of situations in general relativity as well as in the AdS/CFT correspondence. One can define a set of global charges that form the "energy-momentum vector", by analogy with the ADM mass of an asymptotically Euclidean manifold. I will review positivity and rigidity results known as "positive mass theorems" proven by Wang and Chrusciel-Herzlich, under a pointwise positive curvature condition and a completeness assumption. I will then focus on some properties of the "mass aspect tensor" (joint work with M. Dahl and R. Gicquaud) and will present the construction of a family of asymptotically hyperbolic metrics which enjoy particularly nice properties and can have any prescribed energy-momentum vector, thus providing counter-examples to the positive mass theorem without the completeness assumption.
On the mass of asymptotically hyperbolic manifoldsread_more
HG G 43
19 March 2013
15:15-16:15 		Vincent Millot
Université de Paris 7
Event Details

Analysis Seminar

Title Asymptotics for a fractional Ginzburg-Landau equation in arbitrary dimensions
Speaker, Affiliation Vincent Millot, Université de Paris 7
Date, Time 19 March 2013, 15:15-16:15
Location HG G 43
Abstract In this seminar, I will present some recent results on the asymptotic analysis of a fractional version of the Ginzburg-Landau equation in bounded domains, where the Laplacian is replaced by an integro-differential operator related to the square-root Laplacian as defined in Fourier space. In the singular Ginzburg-Landau limit, solutions converge weakly to sphere valued 1/2-harmonic maps, i.e., fractional analogues of the usual harmonic maps. However strong convergence may fail and energy concentration may occur. I will explain how to prove such a convergence result and how to derive some geometric properties of the possible concentration set. This is a joint work with Yannick Sire.
Asymptotics for a fractional Ginzburg-Landau equation in arbitrary dimensionsread_more
HG G 43
9 April 2013
15:15-16:15 		Roberto Camassa
University of North Carolina
Event Details

Analysis Seminar

Title Some fundamental issues in internal wave dynamics
Speaker, Affiliation Roberto Camassa, University of North Carolina
Date, Time 9 April 2013, 15:15-16:15
Location HG G 43
Abstract One of the simplest physical and mathematical setups supporting internal wave motion is that of a stratified incompressible Euler fluid filling the domain between two rigid horizontal plates. This talk will present asymptotic models capable of describing large amplitude wave propagation in this environment, and in particular of predicting the occurrence of self-induced shear instability in the waves' dynamics. Some curious properties of the Euler setup for laterally unbounded domains revealed by the models, and confirmed by exact Euler system results, will be discussed.
Some fundamental issues in internal wave dynamicsread_more
HG G 43
23 April 2013
15:15-16:15 		Prof. Dr. Enno Lenzmann
Universität Basel
Event Details

Analysis Seminar

Title Local Monotonicity Formulae and ODE-type theorems for the fractional Laplacian
Speaker, Affiliation Prof. Dr. Enno Lenzmann, Universität Basel
Date, Time 23 April 2013, 15:15-16:15
Location HG G 43
Abstract We will present a local monotonicity formula for a general class of nonlocal pseudo-differential operators. By using this, we derive ODE-type theorems (in the spirit of Picard-Lindelöf and Sturm) for radial solutions of linear and nonlinear elliptic problems with the fractional Laplacian in arbitrary space dimension. In particular, we prove a uniqueness conjecture about nonlinear ground states in any space dimension, which was posed by Kenig-Martel-Robbiano and Weinstein. Time permitting, we will also discuss applications to blowup problems for nonlinear dispersive equations as well as geometric settings in hyperbolic space. This talk is based on joint work with Rupert Frank (Caltech) and Luis Silvestre (U Chicago)
Local Monotonicity Formulae and ODE-type theorems for the fractional Laplacian read_more
HG G 43
30 April 2013
15:15-16:15 		Prof. Dr. Thomas Kappeler
Universität Zürich
Event Details

Analysis Seminar

Title Large number of particles asymptotics of Toda chains
Speaker, Affiliation Prof. Dr. Thomas Kappeler, Universität Zürich
Date, Time 30 April 2013, 15:15-16:15
Location HG G 43
Abstract For data close to the equilibrium, we describe the asymptotics of the dynamics of periodic Toda chains as the number N of particles tends to infinity. These asymptotics involve two KdV equations, one for each of the two possible directions of propagation. This is joint work with Dario Bambusi and Thierry Paul.
Large number of particles asymptotics of Toda chainsread_more
HG G 43
7 May 2013
15:15-16:15 		Dr. Ben Sharp
Imperial College, London
Event Details

Analysis Seminar

Title Interior and free boundary regularity for Dirac-harmonic maps, harmonic maps and related PDE
Speaker, Affiliation Dr. Ben Sharp, Imperial College, London
Date, Time 7 May 2013, 15:15-16:15
Location HG G 43
Abstract Since Hélein's celebrated proof for the regularity of weakly harmonic maps from surfaces to Riemannian manifolds there have been huge improvements and generalisations to the theory, with applications in many areas of analysis and geometry. Notably the work of Tristan Rivière has provided analytical insight to these problems leading to suitable generalisations. In this talk we will give an overview of some of these ideas and present new theorems leading to proofs (and hopefully some insight) for both new and classical results. Some of the work presented is joint with Peter Topping (Warwick) and separately Miaomiao Zhu (MPI Leipzig)
Interior and free boundary regularity for Dirac-harmonic maps, harmonic maps and related PDEread_more
HG G 43
14 May 2013
15:15-16:15 		Dr. Remi Schweyer
Université de Toulouse
Event Details

Analysis Seminar

Title Blow-up dynamics for the semilinear heat flow in the critical energy case
Speaker, Affiliation Dr. Remi Schweyer, Université de Toulouse
Date, Time 14 May 2013, 15:15-16:15
Location HG G 43
Abstract After a short presentation of previous results on the semilinear heat flow, I will focus on the critical energy case. In particular, I will give a theorem in four dimension in the radial case. Moreover, I will construct an approximate solution in all dimensions to obtain a conjecture on the existence of type II blow-up in finite time.
Blow-up dynamics for the semilinear heat flow in the critical energy caseread_more
HG G 43
21 May 2013
15:15-16:15 		Dr. Yannick Sire
Université Aix-Marseille
Event Details

Analysis Seminar

Title Paralinearization theorem on manifolds
Speaker, Affiliation Dr. Yannick Sire, Université Aix-Marseille
Date, Time 21 May 2013, 15:15-16:15
Location HG G 43
Abstract In this joint work with F. Bernicot, we introduce a new bilinear operator which allows, on a manifold with sub-laplacian structure, to derive a paralinearization theorem. I will give an application to a quasi-linear wave equation.
Paralinearization theorem on manifoldsread_more
HG G 43
28 May 2013
15:15-16:15 		Prof. Dr. Olivier Ley
University of Rennes
Event Details

Analysis Seminar

Title Large time results for some degenerate Hamilton-Jacobi equations
Speaker, Affiliation Prof. Dr. Olivier Ley, University of Rennes
Date, Time 28 May 2013, 15:15-16:15
Location HG G 43
Abstract We present recent results on the asymptotics of second-order Hamilton-Jacobi equations in the periodic setting. We assume that the diffusion matrix vanishes in some subset S and is invertible outside S. This subject was extensively studied in the first-order totally degenerate case (when S is the whole set) or in the uniformly parabolic case (when S is empty). The aim is to make the link between these previous works to tackle the issue of general second-order degenerate parabolic Hamilton-Jacobi equations. This is a joint work with V. D. Nguyen (Rennes).
Large time results for some degenerate Hamilton-Jacobi equations read_more
HG G 43
28 May 2013
16:30-17:30 		Dr. Esther Cabezas-Rivas
Universität Münster
Event Details

Analysis Seminar

Title A generalization of Gromov’s almost flat manifold theorem
Speaker, Affiliation Dr. Esther Cabezas-Rivas, Universität Münster
Date, Time 28 May 2013, 16:30-17:30
Location HG G 43
Abstract Taking as an starting point a question by John Lott about the vanishing of the $\hat A$-genus for spin almost-non-negatively curved manifolds, we found a generalization of Gromov’s almost flat manifold theorem where $L^\infty$ bounds for the curvature are relaxed to mixed curvature bounds. During the talk, we will give the precise statement of our theorem and a detailed sketch of the proof. This is a joint work with Burkhard Wilking.
A generalization of Gromov’s almost flat manifold theoremread_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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