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Spring Semester 2012

Date / Time Speaker Title Location
28 February 2012
15:15-16:15 		Dr. Thomas Wannerer
ETH Zurich, Switzerland
Event Details

Analysis Seminar

Title Hermitian area measures
Speaker, Affiliation Dr. Thomas Wannerer, ETH Zurich, Switzerland
Date, Time 28 February 2012, 15:15-16:15
Location HG G 43
Abstract In recent years valuation theory has expanded well beyond the classical framework of convex geometry and has proved to be a useful tool in integral geometry. We explain how area measures arise as the first variation of smooth valuations and show that the space of all area measures is a module over smooth valuations. In view of applications to the integral geometry of complex space forms, we explicitly determine the module structure of Hermitian area measures.
Hermitian area measuresread_more
HG G 43
20 March 2012
15:15-16:15 		Prof. Dr. Jean-Yves Chemin
Université Paris 6
Event Details

Analysis Seminar

Title Large slowly varying global solutions to the incompressible Navier-Stokes equations
Speaker, Affiliation Prof. Dr. Jean-Yves Chemin, Université Paris 6
Date, Time 20 March 2012, 15:15-16:15
Location HG G 43
Abstract In this talk, we are going to recall the concept of large initial data based on the Koch and Tataru theorem for initial data in the space $BM0^{-1}$. THen, we are going to investigate the case of large initial data with slow variation in one direction. After a rescaling, we study an analogous of incompressible Navier-Stokes system with very small viscosity in one direction and with a perturbed pressure term which makes to the system (probably) illposed. Then to bypass the difficulty, we introduced a global Cauchy-Kovalevska method which allows to solve global the rescaled system for small analytic initial data (which correspond to very large initial data in the original problem).
Large slowly varying global solutions to the incompressible Navier-Stokes equationsread_more
HG G 43
17 April 2012
15:15-16:15 		Reto Müller
Imperial College, London
Event Details

Analysis Seminar

Title A family of fourth-order gradient flows on three-manifolds
Speaker, Affiliation Reto Müller, Imperial College, London
Date, Time 17 April 2012, 15:15-16:15
Location HG G 43
Abstract We study the family of gradient flows of the quadratic functionals obtained by integrating |Rc|^2 - 3a/8 R^2 over a closed three-manifold, where Rc and R denote the Ricci and scalar curvature, respectively, and a is a nonnegative parameter. For a<1, we obtain short-time existence for the corresponding flows with a standard DeTurck trick, while for a>1 one cannot obtain short-time existence in general. Our main focus will be on the interesting boundary case a=1. This is joint work with Roberta Alessandroni and Zindine Djadli.
A family of fourth-order gradient flows on three-manifoldsread_more
HG G 43
24 April 2012
15:15-16:15 		Prof. Dr. Erwan Faou
Université de Rennes, France
Event Details

Analysis Seminar

Title 2D NLS on the torus: A zoological approach
Speaker, Affiliation Prof. Dr. Erwan Faou, Université de Rennes, France
Date, Time 24 April 2012, 15:15-16:15
Location HG G 43
Abstract The goal of this talk is to describe qualitative behaviors of some solutions of the cubic nonlinear Schrödinger equation on the two-dimensional torus, and to show how numerical simulations can help to build rigorous mathematical proofs. I will first discuss the possibilities and limits of computer simulations, and then discuss mathematically and/or numerically three types of behaviors: the possibility of energy cascades and growth of Sobolev norms, Nekhoroshev-like stability around plane waves, and the existence of periodic solutions with arbitrarily high Sobolev norms.
2D NLS on the torus: A zoological approach read_more
HG G 43
8 May 2012
15:15-16:15 		Dr. Emanuele Spadaro
MPI Leipzig
Event Details

Analysis Seminar

Title "Mean-convex sets and global barriers to minimal hypersurfaces". >
Speaker, Affiliation Dr. Emanuele Spadaro, MPI Leipzig
Date, Time 8 May 2012, 15:15-16:15
Location HG G 43
Abstract In this talk I will present some results about the relations between mean-convex sets and global supersolutions to the Plateau problem. We will show that these two notions do not coincide in any reasonable sense. Then, starting from this, we will characterize the least global barrier to minimal hypersurfaces with boundary on a given set of $\mathbb{R}^n$, $n\leq 7$, in terms of a constrained mean curvature flow with obstacle.
"Mean-convex sets and global barriers to minimal hypersurfaces". > read_more
HG G 43
15 May 2012
15:15-16:15 		Mircea Petrache
ETH Zürich
Event Details

Analysis Seminar

Title A Plateau problem for U(1)-bundles in 3 dimensions
Speaker, Affiliation Mircea Petrache, ETH Zürich
Date, Time 15 May 2012, 15:15-16:15
Location HG G 43
Abstract We will present an analogue of the Plateau problem where possibly singular U(1)-bundles replace 2D surfaces. The main motivation is the search for a variational formulation of Yang-Mills theory in supercritical dimensions, and we present an answer to this quest in the case of abelian structure groups. The relevant closure theorem (analogous to the closure theorem for integral currents) needed in order to apply the direct method of the calculus of variations is proven by a slicing argument as in Ambrosio-Kirchheim and Hardt-Riviere. The regularity theory for minimizers utilizes instead a new combinatorial argument based on the max-flow min-cut theorem and relies on Smirnov's decomposition of 1-currents.
A Plateau problem for U(1)-bundles in 3 dimensionsread_more
HG G 43
22 May 2012
15:15-16:15 		Prof. Dr. Gianluca Crippa
Universität Basel
Event Details

Analysis Seminar

Title Two uniqueness results for the two-dimensional continuity equation with velocity having L^1 or measure curl
Speaker, Affiliation Prof. Dr. Gianluca Crippa, Universität Basel
Date, Time 22 May 2012, 15:15-16:15
Location HG G 43
Abstract In this seminar I will present two results regarding the uniqueness (and further properties) for the two-dimensional continuity equation and the ordinary differential equation in the case when the vector field is bounded, divergence free and satisfies additional conditions on its distributional curl. Such settings appear in a very natural way in various situations, for instance when considering two-dimensional incompressible fluids. I will in particular describe the following two cases: (1) The vector field is time-independent and its curl is a (locally finite) measure (without any sign condition). (2) The vector field is time-dependent and its curl belongs to L^1. Based on joint works with: Giovanni Alberti (Universita' di Pisa), Stefano Bianchini (SISSA Trieste), Francois Bouchut (CNRS & Universite' Paris-Est-Marne-la-Vallee) and Camillo De Lellis (Universitaet Zuerich).
Two uniqueness results for the two-dimensional continuity equation with velocity having L^1 or measure curl read_more
HG G 43
29 May 2012
15:15-16:15 		Luca Martinazzi
Rutgers University, USA
Event Details

Analysis Seminar

Title "The relaxed energy for harmonic maps from B^3 into S^2"
Speaker, Affiliation Luca Martinazzi, Rutgers University, USA
Date, Time 29 May 2012, 15:15-16:15
Location HG G 43
Abstract I will discuss the relaxed Dirichlet energy for maps from B^3 into S^2 (definitions, meaning, etc... ), treating the regularity of minimizers in particular. This field contains several long standing open questions. I will present a recent result which gives us a better understanding of the minimizers of this energy, and casts even more open questions.
"The relaxed energy for harmonic maps from B^3 into S^2" read_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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