Apr 16, 2015 
Informal Meeting

Planning 
Suggestions of topics and schedule

Apr 23, 2015 
Anna Karnauhova (Free University Berlin) 
The Origin of the YangBaxter Equation  Yang's Approach (Reading session) 
The aim of the reading session consists in clarifying Yang's approach for obtaining exact results for the manybody problem presented in the following paper:
C. N. Yang: "Some Exact Results for the ManyBody Problem in one Dimension with Repulsive DeltaFunction Interaction"
Phys. Rev. Lett. 19, 1312  Published 4 December 1967

Apr 30, 2015 
Nicola Vassena (Free University Berlin) 
Monomolecular reaction networks: a new proof of flux transitivity 
At first, I will briefly recall the flux influence theorem by Fiedler and Mochizuki. It describes, in terms of the network structure only, which reaction rates
j' respond to perturbation of a reaction rate j*. This theorem has been proved to be transitive. Since proving this transitivity turned out to be more involved
than expected, I will define some new tools for dealing with these particular networks. These tools are related to standard connectivity concepts from
graph theory, and Menger's theorem in particular. Using them, I will reformulate the flux influence theorem and prove its transitivity in a simplified way.

May 7, 2015 
Mark Curran (Free University Berlin) 
ReactionDiffusion Equations with Spatially Distributed Hysteresis
in Higher Spatial Dimensions 
Many chemical and biological processes are modelled by reactiondiffusion equations with a nonlinearity involving hysteresis. In such problems each
spatial point can be in one of two configurations and the configuration changes in time via a hysteresis law. Points in different configurations segregate
the domain into several subdomains and switching implies that these subdomains are separated by free boundaries. We will discuss how the hysteresis
gives rise to a novel type of free boundary evolution.

May 21, 2015 
Dominik Otto (Free University Berlin) 
Determining nodes in regulatory networks 
Yuya Tokuta (Free University Berlin) 
Bioconvection with nonisotropic lateral taxis generated by Euglena gracilis 
Konstantinos Zemas (Free University Berlin) 
Spatially discrete reactiondiffusion equations with discontinuous hysteresis 
May 28, 2015 
Judith Lehnert (Technical University Berlin) 
Adaptive control of synchronization in delaycoupled networks 
The focus of this talk will be on adaptive control methods, which allow for controlling dynamical systems in situations where parameters
drift or are unknown. I will suggest two adaptive control schemes to control zerolag and cluster synchronization in delaycoupled StuartLandau oscillators.
The first method relies on the adaptation of the phase of the complex coupling strength, while for the second method I adapt the topology of the network in order to reach the target state.

June 4, 2015 
Bernhard Brehm (Free University Berlin) 
Expanding measures in Bianchi Class A Cosmologies 
We will give a short introduction to the Bianchi system of ODE and recall the estimates derived last time in November, as well as a gentle introduction to some tools about differential forms and measure theory.
Then we will discuss an expanding measure (volume form) for the Bianchi flow and its Poincaremaps. Using November's estimates and the expanding measure,
we prove that Lebesgue almost every solution forms particle horizons (in practice, this means that the solution converges almost exponentially fast to the attractor).

June 11, 2015 
Phillipo Lappicy (Free University Berlin) 
On the zero number property for singular scalar parabolic equations 
One of the main tools to understand the dynamics of scalar parabolic equations is the zero number property.
This property dates back to Sturm, and was reformulated by Matano, Angenent, Fiedler and others. More recently,
Chen and Polacik proved a version of this property in the case that the equation displays a coefficient which is singular at one boundary point.
On this talk, I explain the main ingredient of Angenent's proof (without any singular term) and how this was modified by Polacik
(with a singular term). Lastly, I will present how these ideas can be used to prove the case of two singularities.

June 18, 2015 
Nicola Vassena (Free University Berlin) 
Monomolecular reaction networks: A new proof of flux transitivity (Poster) 
Phillipo Lappicy (Free University Berlin) 
The dynamics of axially symmetric solutions for dissipative parabolic equations on the sphere (Talk) 
Nikita Begun (Free University Berlin) 
Stability of hyperbolic attractors (Poster) 
Juliette Hell (Free University Berlin) 
Dynamics of the MAPkinase Cascade (Talk) 
June 25, 2015 
Ignite Talks

We will have a special afternoon filled with ''ignite talks''! 
An ignite talk consists of 20 slides which autoforward every 15 seconds. Hence every talk lasts exactly 5 minutes. The main point is that there
will be large breaks between the blocks of multiple ignite talks for personalized and informal followupdiscussions. We will also provide drinks,
small snacks and enough room for the discussion sessions.
Please find our schedule here!
We will collect all the ignite talks on Tuesday, June 23, so that we can prepare the blocks of multiple talks. Please send your slides in PDF
format by Monday June 22nd at the latest.
We hope that many of you would like to participate so that there will be a firework of ideas, problems and results which we can discuss!

July 2, 2015 
Robert Krehl (FU Berlin)

Das Fucik Spektrum unter verschiedenen Randwertbedingungen 
Xiaobei Ma (FU Berlin)

Deciding Hopf Bifurcations by Quantifier Elimination 
Sascha Siegmund (FU Berlin)

Different approaches to flux sensitivity analysis in chemical reaction networks 
Ismail Yenilmez (FU Berlin)

Weak Solutions of Conservation Laws

Students present their progress in Master/Bachelor Thesis.

July 9, 2015 
Dr. Nikita Begun (Free University Berlin) 
Stability of hyperbolic attractors 
The dynamical object which we study is a compact invariant set with a suitable hyperbolic structure.
Stability of hyperbolic attractors was studied by Pliss and Sell. They assumed that the neutral and the stable
linear spaces of the corresponding linearized systems satisfy Lipschitz condition. They showed that if a perturbation
is small, then the perturbed system has a hyperbolic attractor KY, which is homeomorphic to the hyperbolic attractor
K of the initial system, close to K, and the dynamics on KY is close to the dynamics on K. At the same time, it is known
that the Lipschitz property is too strong in the sense that the set of systems without this property is generic. Hence, there
was a need to introduce new methods of studying stability of hyperbolic attractors without Lipschitz condition. We will show
that even without Lipschitz condition there exists a continuous mapping h such that h(K) = KY.

July 16, 2015 
Hannes Stuke (Free University Berlin) 
Attractors, blowup and real imaginary afterlife 
In my talk I will present theorems connecting the attractor and blowup of solutions in analytic systems.
I will discuss the case of the saddlenode bifurcation and indicate how to prove, that for example in the nonlinear
heat equation it is possible to continue the solution onto the real axis through imaginary time after blowup.
