Nonlinear Dynamics at the Free University Berlin

Winter 2018/2019

Oberseminar Nonlinear Dynamics



Tuesday, October 16, 2018 Jan Sieber (University of Exeter) A nonsmooth saddle-node in a non-autonomous dynamical system"
Tuesday, November 6th, 2018 Lutz Schimansky-Geier (Humboldt-University at 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 self-navigating 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 so-called 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. Please note that the seminar takes place at 2:15 p.m. at TU Berlin, Str. des 17. Juni 135, in lecture room MA415, 10623 Berlin.
Tuesday, November 20th WIAS International Workshop: Dynamics of Coupled Oscillator Systems
Tuesday, December 4th dies academicus
Tuesday, January 15th Prof. Willie Hsia (National Taiwan University) On the mathematical analysis of the synchronization theory with time-delayed effect
In this lecture, we will introduce a newly developed mathematical theory on the synchronized collective behavior of the Kuramoto oscillators with time-delayed interactions and phase lag effect. Both the phase synchronization and frequency synchronization are in view. This is joint work with Bongsuk Kwon, Chang-Yeol Jung and Yoshihiro Ueda.
Tuesday, January 22nd Edgard Pimmentel ( 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 state-dependent degenerate problems and report recent (optimal) results. We close the talk with a discussion on open problems and further directions of work.

Time and Place

Talks usually take place on Tuesday at 3:15 p.m. at Freie Universität Berlin, Arnimallee 3, Room 130, 14195 Berlin.

Tea/coffee will be served at 2:45 136.
Guests are always welcome !


switch Last change: Jan. 10, 2019
This page strictly conforms to the XHTMLswitch1.0 standard and uses style sheets. Valid XHTML 1.0! Valid CSS!