The Dynamic Analysis seminar is organized jointly with the analysis group at the UvA.

The seminar (usually) takes place every other Wednesday, 16:00-17:00.

Talks are intended for an audience with a background in analysis and dynamical systems, including PhD students.

For more information, please contact the organizers: Oliver Fabert (VU), Rob van der Vorst (VU), Han Peters (UvA) and Ale Jan Homburg (UvA).

A database of earlier years' seminars can be found here.

## Upcoming talks in 2017

13 September @VU: **Thomas Rot** (Köln), 16:00-17:00

*Title:* The classification of proper Fredholm maps up to proper homotopy

*Abstract:*In the fifties Pontryagin showed that homotopy classes of maps into spheres are in one to one correspondence with framed cobordism classes of the domain. This correspondence enabled him to compute the homotopy groups $\pi_{n+k}(S^n)$ for small values of k. In this talk I will discuss extensions of these ideas to infinite dimensions. This is joint work with Alberto Abbondandolo.

27 September: **Emmanuel Opshtein** (Strasbourg), 16:00-17:00

*Title:* TBA

*Abstract:* TBA

11 October: **Andres Pedroza** (Colima), 16:00-17:00

*Title:* TBA

*Abstract:* TBA

## Previous talks in 2017

16 August @VU: **Tom van den Bosch** (VU), 16:00-17:00, WN-M639

*Title:* Stochastics of growing and persisting cell populations

*Abstract:* Some cellular populations contain subpopulations which exhibit a phenotypic switch to become dormant. These persister cells do not grow, but are able to survive outside stress to reduce the risk of total populations extinction. However, the rates at which cells switch their phenotype is a random variable, and as such the number of persisters shows stochasticity. Because of this, there is a nonzero probability that a population contains no persisters, thus being at risk. In this paper we aim to study this risk. We first derive a master equation for the persister cell model. Since fractions of persister cells are usually low, the persister model is very similar to the exponential growth process, of which we derive an exact probability distribution. Using this, we derive the probability generating function of a simplified model for persisters, which we show to be accurate for low fractions. We then fit distributions to data generated by the Gillespie algorithm to show the distribution of persister cells. Lastly, we solve the master equation for the first and second moments to derive expressions for the fraction of persister cells and the noise in the number of cells. With this fraction we derive an exact probability distribution for a model in which the fraction is constant.

21 June @VU: **Tomas Dohnal** (Dortmund), 16:00-17:00, Room **S-623**

*Title:*Rigorous Asymptotics of Moving Pulses for Nonlinear Wave Problems in Periodic Structures*Abstract:*The possibility of moving, spatially localized pulses of constant or time periodic form in periodic media, e.g. in photonic crystals, is interesting from the mathematical as well as the applied point of view. An example is optical computing where such pulses could function as bit carriers. Pulses in the form of asymptotically small and wide wavepackets can be studied with the help of envelope approximations. Hereby the envelope satisfies an effective equation with constant coefficients. Rigorous results of such approximations in one spatial dimension on long time intervals for the periodic nonlinear Schrödinger equation will be presented but also the current work on the two dimensional analog will be briefly discussed. We concentrate on the asymptotic scaling which leads to the, so called, coupled mode equations (CMEs) of first order. CMEs have families of solitary waves parametrized by velocity, such that in the original model propagation of localized pulses is possible for a range of velocities at one fixed frequency. The justification proof relies on the Bloch transformation, Sobolev space estimates and the Gronwall inequality. Besides the idea of the proof we present also some numerical examples.

24 May @VU: **Klaus Mohnke** (HU Berlin), 16:00-17:00, Room **S-623**

*Title:* Counting holomorphic curves with jet conditions

*Abstract:* I will discuss constraints on higher derivatives of (pseudo)holomorphic curves. The number of such curves seems to be elusive. I will explain why this is not surprising. The advantage of higher order conditions over simple tangency conditions will be demonstrated on an application to Lagrangian embedding problems.

26 April @VU: **Erik Steur** (Eindhoven), 16:00-17:00, Room M-655

*Title:* Partially synchronous oscillations in networks of time-delay coupled systems*Abstract:* Synchronization in networks of interacting systems (species, entities, ...) is profound in nature and finds many interesting applications in engineering. Examples include the simultaneous flashing of fireflies, the synchronized release of action potentials in networks of neurons in the brain, orbital locking in solar systems and coordinated motion in groups of robots. Often such networks show a form of incomplete synchronization that is characterized by the asymptotic match of the states of some, but not all of its systems. Necessary for this type of synchronization, which we call partial synchronization, is the existence of partial synchronization manifolds, which are linear invariant manifolds in the state-space of the network of systems. We present a number of conditions for the existence of partial synchronization manifolds for networks of systems that interact via time-delay coupling functions. Next we discuss local and global stability of partial synchronization. We support our findings with numerical simulations of networks of time-delay coupled Hindmarsh-Rose model neurons. This is joint work with Henk Nijmeijer, Sasha Pogromsky and Wim Michiels.

29 March @VU: **Maria Westdickenberg** (Aachen), 16:00-17:00, Room **C-147**

*Title:* Energy methods for existence and evolution

*Abstract:* For many PDE it is useful to view the phase space as a complex energy landscape. Solutions of static problems may be viewed as local minima or saddle points of the energy. For time-dependent PDE with a gradient flow structure, energy dissipation can be used to understand qualitative and quantitative properties of solutions. We give an overview of some well-known and newer results in this area, including the use of Gamma-limits to show existence of local minima and the use of energy and dissipation to quantify rates of coarsening, relaxation, and metastable evolution.

15 March @VU: **Richard Siefring** (Bochum), **15:30-16:30**, Room M-655

*Title:* Slice orbits and a dynamical characterization of the 4-ball

*Abstract:* We give a characterization of symplectic manifolds with boundary which are symplectomorphic to star-shaped regions in (R^4, \omega_0) in terms of topological-dynamical properties of orbits on the boundary. As a corollary we prove that certain transverse knots cannot appear as periodic orbits of the Reeb vector field for a dynamically convex contact form on tight S^3. This is joint work with Umberto Hryniewicz and Pedro Salomao.

01 March @VU: **Chiara Gallarati** (Delft), 16:00-17:00, Room M-655

*Title:* Maximal L^p-regularity for parabolic equations with measurable dependence on time.

*Abstract:* In this talk I will introduce the concept of maximal L^p-regularity and explain a new approach to maximal L^p-regularity for parabolic PDEs with generator A(t) that depends on time in a measurable way. As an application I will obtain optimal L^p(L^q) estimates, for every p,q\in\(1,\infty), for systems of non-autonomous differential equations of order 2m. This is a joint work with Mark Veraar (TU Delft).

15 February @VU: **Oliver Tse** (Eindhoven), 16:00-17:00, Room M-655

*Title:* Equilibration in Wasserstein distance for damped Euler equations with interaction forces

*Abstract:* This talk describes the techniques used to provide convergence to (global) equilibrium in the 2-Wasserstein distance of partially damped Euler systems under the influence of external and interaction potential forces.