| Oct 20, 2011 |
Bernhard Brehm
(Freie Universität Berlin) |
Measure-theoretic estimates for Bianchi cosmologies |
| Nov 10, 2011 |
Stefan Liebscher
(Freie Universität Berlin) |
Local passage near the Kasner circle in cosmologial models of Bianchi
type with magnetic field |
| Nov 17, 2011 |
Abderrahim Azouani
(Freie Universität Berlin) |
Feedback control of nonlinear dissipative systems |
I will start by reaction-diffusion paradigm to design a feedback control that stabilizes the unstable solution, for example, either by
observing the values of the solutions at certain nodal points, local
averages of the solutions, or by observing many of their Fourier modes.
Another interesting example is the Navier-Stokes equations. The feedback
control is designed in order to force the solution to converge to the
steady state solution. An appropriate upper bound N of the determining
nodes to stabilize the solutions of the Navier Stokes is derived in terms
of Grashof number.
Discrete data assimilation inserts the observational measurements of
the reference dynamical system into an approximate solution. I will
discuss this idea, which is used to initialize a weather forecasting model.
|
| Nov 24, 2011 |
Juliette Hell, Alexey Osipov
(Freie Universität Berlin) |
Shadowing lemmas and Conley index |
|
Standard shadowing lemma claims that a dynamical system
has a shadowing property in a small neighborhood of a hyperbolic set
(i.e. in this neighborhood any sufficiently precise ''approximate solution''
is ''close'' to some exact solution).
In this talk we will try to look at shadowing from a topological point of view.
Our talk will be mostly based on papers of Conley and Easton.
We will describe Conley's way of proving standard shadowing lemma, which
reduces the problem to studying sequences of mappings of ''squares''.
We will speak about Easton's strategy of shadowing pseudotrajectories
(i.e. ''approximate solutions'') via ''chains of windows''.
Besides, we will discuss possible modifications of this results
for a certain non-standard shadowing property, which naturally arises,
when one tries to transfer standard shadowing property via compactification/decompactification
technique (e.g. Poincare compactification).
|
| Dec 01, 2011 |
Ernesto Nungesser
(Albert-Einstein-Institute Golm) |
Late-time behaviour of the Einstein-Vlasov system with Bianchi symmetry |
|
In the beginning of the talk I will introduce the Einstein equations on a mass shell and the Vlasov equation in the case of Bianchi symmetry. In the second part of the talk I will discuss the methods used to obtain the main results which concern the late-time behaviour assuming small data for certain Bianchi types.
|
| Dec 08, 2011 |
Ksenia Darovskaya
(Peoples' Friendship University, Moscow) |
A priory estimates of solutions for a differential operator with integral conditions |
|
We consider an ordinary differential equation of the second order with a spectral parameter and integral conditions of several types. For each type of conditions, an a priory estimate of solutions for sufficiently large values of the parameter is proved. As a consequence, sufficient conditions of the Fredholm solvability for such problems are obtained.
|
Dina Kalinichenko
(St. Petersburg State University) |
Free boundary two-phase inductive heating problem |
|
The inductive heating process is considered. The free boundary two-phase inductive heating problem is modeled. An application of a small parameter method is discussed.
|
| Dec 15, 2011 |
Alan Rendall
(Albert-Einstein-Institute Golm) |
Multiple steady states in a dynamical system arising in immunology |
|
The subject of this talk is a four-dimensional dynamical system with a large
number of parameters modelling certain aspects of the immune system
(interaction of T cells and macrophages). The main result is that for
certain large subsets of the parameter space this system has at least seven
stationary solutions. The method of proof is to guess the position of a
stationary solution and then prove the correctness of the guess by a fixed
point argument. The steady states which were not previously known represent
a possible therapeutic target in the treatment of autoimmune or infectious
diseases.
|
| Jan 12, 2012 |
Lev Lazar
(University of Hamburg) |
On conducted and current research of the Neurology of the Visual Perception |
Attempts to comprehend the system of visual perception are neither new
nor rare. Anyway, the underlying processes are yet to understand. In
last twenty years a huge progress is been made in this field by the
cooperative work of Biologists, Neurophysicians, Neuropharmacologists,
Molecular Biologists, Computer Scientists and Mathematicians.
I'm going to give an overview of research on visual perception and other
relevant, tightly related topics. After a brief discussion of involved
Neurology and Molecular Biology relevant for understanding (not only
from Mathematical point of view) of processes that are finding place in
our central nervous system, I'm going to describe the models and
concepts purposed to qualitatively analyze the neurology of visual
perception, visual cognition and related phenomena.
|
Jan 17, 2012
Tuesday
15:15 |
Stefan Liebscher
(Freie Universität Berlin) |
Invariant manifolds in Maxwell-Bianchi systems |
|
I will concentrate on Lipschitz properties of the local passage near
the Kasner circle with respect to a non-standard metric. This yields
cone conditions needed for a graph-transformation approach. We obtain
unstable manifolds to some Kasner sequences in a more general context
than pure Bianchi VIII/IX. This is joint work with Alan Rendall.
|
| Jan 19, 2012 |
Bernhard Brehm
(Freie Universität Berlin) |
More about Bianchi |
| Jan 26, 2012 |
Johannes Buchner
(Freie Universität Berlin) |
Takens-Linearization for periodic heteroclinic chains in Bianchi IX |
| Feb 09, 2012 |
Alexander Nazarov
(St.Petersburg State University) |
On the sharp constant in the Poincare inequality with three parameters |
|
In the talk, we discuss the problem of finding a sharp constant in the generalized Poincare inequality.
This and some equivalent problems arise in various fields of mathematics.
We mention the problem of optimality of some goodness-of-fit criteria in non-parametric statistics
and the estimation of critical values in the Lagrange problem.
The talk is based on a joint paper with I.V. Gerasimov
|
Last change: Apr. 10, 2012
