The mathematical colloquium of the HHU Düsseldorf takes place on
Friday
16:45  17:45 in room 25.22 HS 5H.
Before the colloquium (from 4:15 p.m.) everybody is invited for tea, coffee and cookies in 25.22.00.53.
13.04.2018 
Jennifer Ryan (HHU Düsseldorf / University of East Anglia).
Abstract.


Exploiting Hidden Accuracy in Data
Numerical simulations produce data that contains hidden information. This hidden information can be exploited to create even more accurate representations of the data. This presentation will address how these more accurate representations of data can be constructed using information from higher order methods for numerical partial differential equations. Although the discussion will be framed in the context of discontinuous Galerkin finite element methods, the techniques demonstrated naturally apply to other methods as well. This presentation will focus on identifying where this hidden accuracy comes from, why the hidden accuracy is important, and what are the different manifestations of the power of this hidden information.

27.04.2018 
Absolventenfeier

04.05.2018 
Florian A. Potra
(UMBC).
Abstract.


A superquadratic variant of Newton's method
We present the first Qsuperquadratically convergent version of Newton's
method for solving operator equations in Banach spaces that requires only
one operator value and one inverse of the Fréchet derivative per
iteration. The Rorder of convergence is at least 2.4142. A semilocal
analysis provides Sufficient conditions for existence of a solution and
convergence. The local analysis assumes that a solution exists and shows
that the method converges from any starting point belonging to an
explicitly defined neighbourhood of the solution called the ball of
attraction.

18.05.2018 
Constanza RojasMolina (HHU Düsseldorf).
Abstract.


Random Schrödinger Operators arising in the study of aperiodic media
In this talk we review some results on random Schrödinger operators, a standard framework for the study of disordered quantum systems and
the absence of wave propagation in random media, a phenomenon known as Anderson localization. Our goal is to apply these results to the study of spectral and dynamical properties of Delone operators, which serve to model aperiodic structures (quasicrystals). As a consequence, we will show that aperiodic media, although usually associated to singular continuous spectrum and anomalous transport, does exhibit often Anderson localization and, in particular, pure point spectrum.

08.06.2018 
Ilir Snopche (HHU Düsseldorf / UFRJ, Rio de Janeiro).
Abstract.


Distribution of test elements in free groups and surface groups
An element x of a group G is called a test element if for any endomorphism ϕ
of G, ϕ(x) = x implies that ϕ is an automorphism. The ﬁrst nontrivial
example of a test element was given by Nielsen in 1918, when he proved that
every endomorphism of a free group of rank 2 that ﬁxes the commutator [x, y]
of a pair of generators must be an automorphism.
In this talk I will discuss the distribution of test elements in free groups
and surface groups.

15.06.2018 
Jochen Heinloth (Universität DuisburgEssen).
Abstract.


Hitchin's fibration: From integrable systems to number theory
About 30 years ago Nigel Hitchin introduced a new class of so called
completely integrable systems. These geometric objects had their origin
in a set of differential equations but surprisingly turn out to have
various alternative descriptions that allow for arithmetic and
topological applications. Thus a wide range of methods have been applied
to get a better understanding of the underlying spaces.
In this talk I will try to explain a little bit about the history of
these spaces and of some of the methods used to study them. After giving
some more recent insights into their geometry I would like to explain
what the P=W conjecture of de Cataldo, Hausel and Migliorini is about,
which gives an unexpected link between two distinct algebraic structures
of the manifolds appearing in Hitchin's construction.

22.06.2018 
Aleksander Iwanow [older english homepage] (Silesian University of Technology, Gliwice).
Abstract.


A model theoretic approach to actions of metric groups on metric spaces
Typical properties of groups formulated in terms of actions on metric
spaces are not axiomatizable. The most important examples of such prop
erties are amenability, property (T) of Kazhdan or property FR that any
continuous isometric action of G on a real tree has a fixed point.
One of substitutes of axiomatizability is the following notion of Ph.Hall.
A class of topological groups K is called bountiful if for any infinite group
G from K and any subset C of G there is H in K which is a subgroup of G,
contains C and the density character of C coincides with the density character
of H.
We introduce a stronger property and verify it in many situations. In
order to realize this we show how isometric actions of metric groups on Hilbert
spaces and real trees can be presented in continuous logic.

29.06.2018 15:30–16:30 
George Willis (University of Newcastle).
Abstract.


Totally disconnected locally compact groups and actions on trees
Locally compact (l.c.) groups are fundamental to many areas of mathematics and their group
structure is important in many of the contexts in which they appear. Each l.c. group divides into
a connected factor and a totally disconnected factor. Understanding connected l.c. groups reduces,
via the solution of Hilberts 5th Problem achieved in the 1950s, to the study of real Lie groups, but a
comparable understanding of t.d.l.c. groups is only now being developed.
Part of this new understanding, analogous the role of eigenvalues and eigenvectors in Lie theory,
is the concept of the scale on the t.d.l.c. group and associated actions of subquotients of the group
on regular trees.

06.07.2018 
Matthias Röger (TU Dortmund).
Abstract.


Interaction of membrane localized reactions and transportdiffusion processes in cells
In biological cells a tight regulation of processes in the cell and on the cell membrane is for many functions of the cell essential.
We introduce different mathematical models in the form of coupled bulksurface reactiondriftdiffusion systems and investigate in particular pattern forming properties.

20.07.2018 
Ariyan Javanpeykar (Johannes GutenbergUniversität Mainz).
