Thursday, October 7th 
Alejandro López Nieto (Freie Universität Berlin) 
Global dynamics of delay equations with monotone feedback

Even the simplest of delay differential equations yield extremely intricate, infinite dimensional dynamical systems. In the talk I will present a constructive method for classifying the global dynamics of a scalar delay equation under symmetry and monotone feedback assumptions.
If time allows, after the first part of the talk, I will discuss the question of global continuation of periodic solutions in general delay equations with monotone feedback.
Any questions and feedback from the audience are extremely welcome and encouraged!

Thursday, October 21st 
Gentaro Masuda (Freie Universität Berlin) 
The analytical basis for nonlocal Floer homology

Recently, the relation between symplectic geometry and delay differential equations has been drawing attention. There is one approach, socalled nonlocal Floer homology, which would estimate the number of (some) periodic orbits of delay differential equations with constant delays.
The construction of Floer homology consists of three parts: Transversality, Compactness, and Gluing. In this talk, we focus on Compactness in the setting of nonlocal Floer homology and discuss asymptotic convergence of nonlocal unregularized gradient flow lines.

Thursday, October 28th 
Bernold Fiedler (Freie Universität Berlin) 
Real chaos, and complex time

Abstract
(PDF)

Thursday, November 4th 
Dennis Chemnitz (Freie Universität Berlin) 
Introducing delay increases the frequency of nonhomogeneous oscillators

In this talk, I will describe how the introduction of delay increases the frequency of nonhomogeneous oscillators. Furthermore, connections of this problem to optimization problems on spaces of measures and linear programming will be explored. This new viewpoint allows both for a simplification of the proof and for generalization to nonperiodic orbits, compared to the work from my master thesis.

Thursday, November 11th 
Alejandro López Nieto (Freie Universität Berlin) 
The nonwandering set in delay equations with monotone feedback

The role of the nonwandering set in the description of the global dynamics of a dynamical system is fundamental.
Particular applications include finding invariant sets, structural stability properties, and the description of bifurcations of global nature.
In the talk, I will address the description of the nonwandering set of a delay equation with monotone feedback. The results presented guarantee the structural stability of the global attractor based purely on local analysis of the periodic solutions and equilibria of the system.

Thursday, November 18th 
Robin Chemnitz (Freie Universität Berlin) 
Signed sensitivity of Markov chains with application to chemical reaction networks

The most generic dynamic on a network could easily be the probability distribution of a Markov chain. It can be described as a linear ODE without any stochastic framework. In my Master's thesis, I studied the sensitivity of the unique equilibrium of such systems. The results can be used to analyse the sensitivity of equilibria in more complex dynamics on networks.

Thursday, November 25th 
Dennis Chemnitz (Freie Universität Berlin) 
Introducing delay increases the frequency of nonhomogeneous oscillators

I will continue my previous talk on the influence of delay on the frequency of a specific type of nonhomogeneous oscillator. Specifically, I will show how one can reformulate the lemma as an optimal transport problem, based on an idea by Alejandro Kocsard. It turns out that this reformulation simplifies the proof significantly.

Thursday, December 2nd 
Alejandro Kocsard (Universidade Federal Fluminense) 
Rotation theory: from the circle to higher dimensions

Rotation theory has its origins in celebrated works of Henri Poincaré on the dynamics of circle homeormorphisms.
Invoking ergodic theory techniques, this theory has been considerably extended to noninvertible maps and to homemorphisms in higher dimensional spaces.
In this talk we shall start surveying some classical facts about Poincaré theory on the circle and then discuss some more recent results about rotation theory on the 2dimensional torus.

Thursday, December 9th 
Danchen He (Freie Universität Berlin) 
Properties of an epidemic model with control interventions

This time I will tell a story of one type of epidemic model, which is rarely mentioned in previous studies. Then I will give some properties that have been proven and properties that may be proven in the following studies.

Tilman Glorius (Freie Universität Berlin) 
Period Mismatch in a Pyragas Controlled System

We attempt an initial investigation into a Pyragas controlled system with an incorrect delay, i.e. the delay chosen in the control scheme does not match the period of the target orbit.

Hauke Sprink (Freie Universität Berlin) 
Stable manifolds for heteroclinic chains in Horava cosmologies

In this talk we give a perspective on results by Liebscher et al who construct stable manifolds for a certain class of heteroclinic chains in the wellknown Bianchi model in general relativity. The aim of our work is to obtain similar results in the parameter dependent Bianchi models within HL cosmology.

Thursday, December 16th 
Phillipo Lappicy (Universidade Federal do Rio de Janeiro) 
Phillipo Lappicy (Universidade Federal do Rio de Janeiro)

We explicitly construct global attractors of fully nonlinear parabolic equations. The attractors are decomposed as equilibria (timeindependent solutions) and heteroclinic orbits (solutions that converge to distinct equilibria backward and forward in time). In particular, we state necessary and sufficient conditions for the occurrence of heteroclinics between hyperbolic equilibria.s

Thursday, January 13th, at 14:15 Berlin time 
JiaYuan Dai (National Chung Hsing University) 
Selective feedback stabilization of GinzburgLandau spiral waves in circular and spherical geometries

The complex GinzburgLandau equation serves as a paradigm of pattern formation. Within circular and spherical geometries, the existence and stability property of GinzburgLandau spiral waves have already been proved. Since many spiral waves are unstable and thereby rarely visible in experiments and numerical simulation, we aim to selectively stabilize certain significant classes of unstable spiral waves. Our tool for stabilization is the control triple method, which generalizes the celebrated Pyragas control to the setting of PDEs. This is joint work with I. Schneider and B. de Wolff.

Thursday, January 20th 
Fan Cheng (Free University Berlin) 
Using curvature flow to prove isoperimetric inequality in space form

In this talk, we want to discuss proving isoperimetric inequality in space form by constructing different curvature flows and showing longtime existence and exponential convergence of the solution to the flow.

Jannik Schlieffen (Free University Berlin) 
Electrodynamical processes in quantum mechanics

We will compute the selfforce of a particle to show how the quantum
potential and the selfforce share features with each other.

Thursday, January 27th 
Nicola Vassena (Free University Berlin) 
Is genericity always generic?

In the applied sciences, a saddlenode bifurcation is often identified with the Jacobian matrix having a zero eigenvalue. The mathematical argument  rarely mentioned  relies on genericity and details or rigorous proofs are even less often presented.
For vector fields with a network structure, I want to clarify why a genericity argument is not always reliable. To this purpose, I will present two (counter)examples of equilibria with a singular Jacobian that fail to satisfy the other saddlenode conditions, for any parameters choice.

Thursday, February 10th 
Jaqueline Mesquita (University of Brasília) 
Linearized instability principle for neutral FDEs with statedependent delays

In this talk, we will prove a linearized instability principle for neutral FDEs with statedependent delays, using invariance of cone. This is joint work with Bernhard LaniWayda.




