Analysis Seminar
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Tuesdays in Hermann-Weyl Zimmer - room HG G 43 - unless otherwise indicated
Spring Semester 2012
| Date |
Speaker |
Title |
Time |
Location |
| 28-feb-2012 (tue) |
Thomas Wannerer
|
Hermitian area measures
|
15:15-16:15 |
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.
|
| Speakers: |
Dr. Thomas Wannerer
(ETH Zürich, Switzerland)
E-Mail:
|
|
| 20-mar-2012 (tue) |
Jean-Yves Chemin
|
Large slowly varying global solutions to the incompressible Navier-Stokes equations
|
15:15-16:15 |
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). |
| Speakers: |
Prof. Dr. Jean-Yves Chemin
(Université Paris 6)
|
|
| 17-apr-2012 (tue) |
Reto Müller
|
A family of fourth-order gradient flows on three-manifolds
|
15:15-16:15 |
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. |
| Speakers: |
Reto Müller
(Imperial College, London)
|
|
| 24-apr-2012 (tue) |
Erwan Faou
|
2D NLS on the torus: A zoological approach
|
15:15-16:15 |
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.
|
| Speakers: |
Prof. Dr. Erwan Faou
(Université de Rennes, France)
|
|
| 8-may-2012 (tue) |
Emanuele Spadaro
|
"Mean-convex sets and global barriers to minimal hypersurfaces". >
|
15:15-16:15 |
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. |
| Speakers: |
Dr. Emanuele Spadaro
(MPI Leipzig)
|
|
| 15-may-2012 (tue) |
Mircea Petrache
|
A Plateau problem for U(1)-bundles in 3 dimensions
|
15:15-16:15 |
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. |
| Speakers: |
Mircea Petrache
(ETH Zürich)
|
|
| 22-may-2012 (tue) |
Gianluca Crippa
|
Two uniqueness results for the two-dimensional continuity equation with velocity having L^1 or measure curl
|
15:15-16:15 |
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). |
| Speakers: |
Prof. Dr. Gianluca Crippa
(Universität Basel)
|
|
| 29-may-2012 (tue) |
Luca Martinazzi
|
TBA
|
15:15-16:15 |
HG G 43 |
| Speakers: |
Luca Martinazzi
(Rutgers University, USA)
|
|
| 5-jun-2012 (tue) |
|
TBA
|
15:15-16:15 |
HG G 43 |
|
|
