| Oct 16, 2008 |
Almut Burchard
(University of Toronto) |
Motion of an infinite elastic curve:
well-posedness, stability of solitary waves, open questions |
| Oct 23, 2008 |
Alexey Teplinsky
(Academy of Sciences, Kiev) |
Herman's theory revisited |
|
For certain range of r and δ we prove
that any Cr-smooth circle diffeomorphism with
irrational rotation number from the Diophantine class Dδ
is Cr-1-δ-smooth conjugate to a rigid rotation.
This is the only sharp result of this kind for today.
In particular, it improves the famous results of M.Herman and his followers.
The proof is tricky but almost elementary.
(Joint work with K.Khanin.)
|
| Oct 30, 2008 |
Sergey Tikhomirov |
Shadowing in smooth flows |
We study the shadowing property of smooth vector fields on a compact
manifold. The shadowing problem is related to the following
question: under which condition for any pseudotrajectory of a flow
generated by vector field there exists a close exact trajectory? The
main difference between the shadowing problem for vector fields and
the similar problem for discrete dynamical systems is related to the
necessity of reparametrization of shadowing trajectories in the
former case.
In this work we study the structure of the C1-interiors of the
sets of vector fields with various shadowing properties. We show
that for the case of Lipschitz shadowing property such a
C1-interior coincides with the set of structurally stable vector
fields. If the dimension of the manifold is less or equal 3, then
the similar statement can be proved for the Oriented shadowing
property.
The main result I present in this talk is an example of not
structurally stable vector field on 4-dimensional manifold that lies
in the interior of the set vector fields with Oriented shadowing
property.
|
| Nov 06, 2008 |
Marc Georgi
(Freie Universität Berlin) |
Travelling waves in the Fermi-Pasta-Ulam lattice |
|
In the talk I will motivate the problem and mainly focus on the
main ingredient in the proof, which is Lin's method.
|
| Nov 13, 2008 |
Bernold Fiedler
(Freie Universität Berlin) |
Aus nichts wird nichts ? |
| Nov 27, 2008 |
Marc Georgi
(Freie Universität Berlin) |
Lin's method |
|
In the talk I will introduce a functional analytic frame-
work, with which one can detect periodic and multi-round homoclinic
orbits near a primary homoclinic orbit. I will mainly
focus on ordinary differential equations but also point out technical
difficulties when it comes to advance delay equations.
|
| Dec 04, 2008 |
Hao Wu
(WIAS Berlin) |
Convergence to Equilibrium for Nonlinear Evolution Equations |
|
In this talk I will present the Lojasiewicz-Simon approach on the
study of convergence to equilibrium for nonlinear evolution equations. Some
applications of this approach will be discussed.
|
| Dec 11, 2008 |
Bernahrd Brehm
(Freie Universität Berlin) |
Invariant measures of the Kasner map |
| Jan 08, 2009 |
Bernd Kawohl
Universität zu Köln |
Variational versus PDE-based Approaches in Mathematical Image Processing |
|
In image processing we are often presented with amazing examples of image
enhancement algorithms. Yet, when applied to different noisy images, they can
product unwanted effects. The analysis of such algorithms lags behind their
intuitive development. Two essentially different models have found wide
recognition: a variational approach according to Mumford and Shah and an
approach via nonlinear diffusion equations. One of these equations is
nonparabolic and was suggested by Perona and Malik. In this short survey I
point out a connection between these two seemingly unrelated approaches and
explain some connection with total variational flow.
|
followed by the colloquium talk
5:15 p.m., Lecture hall 001, Arnimallee 3 |
Gleichdicke, oder warum konvexe Geometrie Leben retten kann |
|
Wann hat ein Rohr einen exakt kreisförmigen Querschnitt? Wenn es aus
jeder Richtung von außen gleich dick zu sein scheint? Das könnte man
mit einer Schieblehre nachmessen, und so gaben es die Vorschriften
der NASA beim Raketenbau vor. Den Verfassern der Vorschriften war
entgangen, dass es geometrische Formen gibt, so genannte
"Gleichdicke", die nicht Kreise sind. Letztlich führte dieser Irrtum
zum Tod einer ganzen Raumschiffbesatzung. Im Vortrag wird dargelegt,
wo uns Gleichdicke im täglichen Leben überall begegnen und welche
interessanten mathematischen Fragen mit ihnen verbunden sind. Der
Vortrag wurde zum Jahr der Mathematik für die mathematisch
interessierte Öffentlichkeit entworfen und richtet sich daher auch an
Hörer aller Semester und anderer Fächer.
|
| Jan 15, 2009 |
Mihaela Enculescu & Juliane Zimmermann
(Max Delbrück Center for Molecular Medicine) |
Modelling actin-based cellular motility |
|
Cell crawling is a vital process, playing an essential role in
embryonic development, wound healing and immune response, but is also
responsible for cancer metastasis. The driving phenomenon of cell
motility is the protrusion of the cell's plasma membrane and the
formation of a thin flat structure at the leading edge of the cell,
called the lamellipodium, by means of actin filaments. Actin is a
highly dynamic biopolymer, that steadily binds monomers at one end
and looses monomers at the other end. We model the formation of a
lamellipodium by calculating the force which the semiflexible actin
filaments exert on the membrane. This force is crucially dependent on
the length of the fluctuating filaments, which are cross-linked at
the inner parts of the lamellipodium thereby forming an "actin gel".
When analyzing the dynamics of the filament's lengths, we obtain
stationary and oscillatory movements. We also solved hydrodynamic
equations to include the velocity of the actin gel into our model. As
we regard the lateral extension of the lamellipodium, we find the
spreading of different wave forms along the plasma membrane. Those
morphodynamic patterns are in good agreement with experimental
results.
|
| Jan 22, 2009 |
Stefan Liebscher
(Freie Universität Berlin) |
Heteroclinic cycles in food-chain models |
| Jan 29, 2009 |
Julia Ehrt
(WIAS Berlin) |
Attractors in hyperbolic equations and parabolic regularizations |
| Feb 05, 2009 |
Abderrahim Azouani
(Freie Universität Berlin) |
P(x)-Laplacian |
| Feb 12, 2009 |
Seminar Unendlichdimensionale Dynamik |
Last change: Mar. 2, 2009
