Tuesday, October 16, 2018 
Jan Sieber (University of Exeter) 
A nonsmooth saddlenode in a nonautonomous dynamical system" 
Tuesday, November 6th 
Prof. em. Dr. Lutz SchimanskyGeier (HumboldtUniversity Berlin) 
Celestial mechanics of fruit flies or a theory for mushroomers 
The topic of global search in complex environments have been often investigated. But a
search can also be local in the sense that it is centered at a given home position. In the latter
case, the searcher does not only look for a new target but is also required to regularly return to
the home position. Such behavior is typical for many insects and achieves technical importance
for selfnavigating robotic systems. We propose a stochastic nonlinear model for local search
which does not distinguish between the two aims. The dynamics bases on an unique pursuit and
escape behavior of the heading from the position vector realizing thereby optimal exploration of
space and the return to the home. We discuss the mechanics of the searcher and inspect the
role of noise. Such randomness is present in the decision making rule of selecting the new heading
direction. We consider Levy noises with different degree of discontinuity and report about
steady spatial densities for the searchers. Also we report about an optimal noise intensity that
a searcher finds a target at nearby places. For this noise value the required time for finding the
target becomes minimal which appears to be the consequence of different relaxation processes
in the spatial and the angular dynamics. Further extensions of the model are discussed during
the lecture.

Tuesday, November 13th 
Hannes Stuke (FU Berlin) 
A dynamical systems approach to outlier robust machine learning 
We consider a typical problem of machine learning  the reconstruction of probability distributions
of observed data. We introduce the socalled gradient conjugate prior (GCP) update and
study the induced dynamical system. We will explain the dynamics of the parameters and show
how one can use insights from the dynamical behavior to recover the ground truth distribution in
a way that is more robust against outliers. The developed approach also carries over to neural
networks.

Tuesday, January 15th 2019 
Prof. Willie Hsia (National Taiwan University) 
On the mathematical analysis of the synchronization theory with
timedelayed effect 
In this lecture, we will introduce a newly developed mathematical theory on the synchronized
collective behavior of the Kuramoto oscillators with timedelayed interactions and phase lag effect.
Both the phase synchronization and frequency synchronization are in view. This is joint work with
Bongsuk Kwon, ChangYeol Jung and Yoshihiro Ueda.

Tuesday, January 22nd 2019 
Edgard Pimentel
(Pontifical Catholic University of Rio de Janeiro) 
Geometric methods in regularity theory for nonlinear PDEs 
In this talk we examine the regularity theory of the solutions to a few examples of nonlinear
PDEs. Arguing through a genuinely geometrical method, we produce regularity results in Sobolev
and Hölder spaces, including some borderline cases. Our techniques relate a problem of interest
to a further one  for which a richer theory is available  by means of a geometric structure, e.g., a
path. Ideally, information is transported along such a path, giving access to finer properties of the
original equation. In the first part of the talk, we cover examples including elliptic and parabolic
fully nonlinear problems, the Isaacs equation and a double divergence model. Then we proceed
to the setting of statedependent degenerate problems and report recent (optimal) results. We
close the talk with a discussion on open problems and further directions of work.

Tuesday, January 29th 2019 
Alejandro Kocsard
(Universidade Federal Fluminense) 
Random walks, synchronization and existence of invariant
measures 
In this talk we start discussing some classical results due to Furstenberg [Fur63] about random
product of matrices and how a certain form of synchronization naturally appears in this
context. Then we shall consider some extensions of these results for random walks on compact
smooth manifolds [Led84, Ant84, Cra90]. Finally we will see how these ideas can be used to
study the existence of invariant (probability) measures for smooth actions on manifolds by some
groups which are a priori nonamenable.

Tuesday, February 5th, 2019 
Alejandro Kocsard
(Universidade Federal Fluminense) 
Random walks, synchronization and existence of invariant
measures II 
In this second talk we will review some results we discussed in the first one, but from a
"dynamical systems" point of view. Finally we shall discuss some applications of these results to
the so called Burnside problem on manifolds.
