Tuesday, October 29th 
Pavel Gurevich and Hannes Stuke (Freie Universität Berlin) 
Reinforcement learning 
Tuesday, November 5th 
Phillipo Lappicy (Universidade de Sao Paulo, Freie Universität Berlin) 
HoravaLifshitz Gravity: Bifurcations and Chaos 
Lorentzian causal structure, general covariance, and scale invariance are first principles that play a key role in the nature of generic spacelike singularities in general relativity. To bring a new perspective on the contributions of these first principles regarding the chaotic aspects of generic singularities, we consider the initial singularity in spatially homogeneous Bianchi type VIII and IX models in HoravaLifshitz gravity, which replaces relativistic first principles with anisotropic scalings of Lifshitz type.
To describe the nature of the initial singularity in these models, we make use of mathematical tools that include symbolic dynamics and chaos. For the present class of models, it is shown that general relativity is a critical case that corresponds to a bifurcation where chaos becomes generic. For different models nearby the general relativistic critical case, Cantor sets and iterate function systems are important for describing the chaotic aspects of generic singularities.
This is joint work with Juliette Hell and Claes Uggla.

Tuesday, November 12th 
Nicolas Perkowski 
From hopping particles to stochastic PDEs 
I will try to give an overview of some of my research interests, focusing on certain a priori ill posed stochastic PDEs and their derivation. An important task in stochastics is to find and construct "universal" models that describe a given phenomenon. For example, any random variable that is given by the superposition of many small independent influences is approximately Gaussian, independently of the concrete nature of the small influences, and therefore we call the Gaussian distribution universal. When trying to derive universal models for phenomena that evolve in space and time, formal calculations often suggest that we should consider nonlinear stochastic PDEs driven by spacetime white noise. This is a problem because due to the irregularity of the noise the solution might be too irregular to make sense of the nonlinearities in the equation. But in recent years we found new ways of overcoming these problems, making sense of the equations, and proving their universality in some cases.

Tuesday, November 19th 
Ralf Toenjes (University of Potsdam) 
The Constructive Role of Noise in The Dynamics on Network Hubs for Network Synchronization 
We describe and analyze a coherence resonance phenomenon for
synchronization in bipartite networks of well connected hubs and
followers when the hubs are subjected to noise. Using the OttAntonsen
ansatz for globally coupled phase oscillators the dynamics of the mean
fields is described by a lowdimensional system of Langevin equations.
Averaging over the fast stochastic dynamics of the hubs yields
ordinary differential equations which predict the coherence resonance
reasonably well.

Tuesday, November 26th 
JiaYuan Dai (National Center for Theoretical Sciences) 
Hyperbolicity of GinzburgLandau vortex solutions 
We prove that each equilibrium of the GinzburgLandau equation restricted on the invariant
subspace of vortex solutions is hyperbolic, that is, its associated linearization possesses nonzero eigenvalues. This result completely describes the global attractor of vortex solutions, and also yields the GinzburgLandau spiral waves of nodal type. This result is a joint work with Dr. Lappicy.

Tuesday, January 14th 
Frits Veerman (University of Heidelberg) 
Toll roads and freeways: Defects in bilayer interfaces in the multicomponent functionalised CahnHilliard equation 
We study a multicomponent extension of the functionalised CahnHilliard equation, which provides a framework for the formation of patterns in fluid systems with multiple amphiphilic
molecules. The assumption of a length scale dichotomy between two amphiphilic molecules allows the application of geometric techniques for the analysis of patterns in singularly perturbed
reactiondiffusion systems. For a generic twocomponent system, we show that solutions to the fourdimensional connection problem provide the leading order approximation for solutions to the
full eightdimensional barrier problem, which can be obtained through a perturbative expansion in the layer width. Moreover, we show that a saddlenode bifurcation of bilayer solutions in the
fourdimensional connection problem acts as a source of socalled defect solutions, i.e. solutions to the barrier problem that are not also solutions to the connection problem. The analysis combines
geometric singular perturbation theory with centre manifold theory in an infinitedimensional context.

Tuesday, January 28th 
Martin Brokate
(TU München) 
Sensitivity results for rate independent evolutions 
Rate independent evolutions are evolutions whose solution operators commute with time
transformations. They are inherently nonlinear and nonsmooth. We present some introduction,
outlining various mathematical approaches as well as relations to other fields. We then address
sensitivity, in particular the question whether the solution operators possess weak differentiability
properties.

Tuesday, February 11th 
Peter Szmolyan (Technische Universität Wien) Cancelled due to illness 
Advances in GSPT  teaching new tricks to an old dog 
Due to the efforts of many people geometric singular perturbation theory (GSPT) has developed into
a very successful branch of applied dynamical systems. GSPT has proven to be very useful
in the analysis of an impressive collection of diverse problems from natural sciences,
engineering and life sciences.
Fenichel theory for normally hyperbolic critical manifolds
combined with the blowup method at nonhyperbolic points is often able to provide remarkably
detailed insight into complicated dynamical phenomena, often even in a constructive way.
Much of this work has been carried out in the framework of slowfast systems in standard form,
i.e. for systems with an a priori splitting into slow and fast variables.
More recently GSPT turned out to be useful for systems for which the slowfast structures
and the resulting applicability of GSPT are somewhat hidden. Problems of this type include
singularly perturbed systems in nonstandard form, problems depending singularly on more
than one parameter and smooth systems limiting on nonsmooth systems as a parameter
tends to zero. Often several distinct scalings must be used to cover the dynamics of interest and
matching of these different scaling regimes is carried out by the blowup method.
In this talk I will survey these developments and highlight some ongoing activities.
