Juli 2021

### 07.07.2021 13:00 Martin Schuster, Oregon State University :Modeling cooperative behavior in bacteriavia ZOOM (Boltzmannstr. 3, 85748 Garching)

Interactions like communication, cooperation and competition abound in the microbial world. They play an important role in natural ecosystems, infection, and agriculture. This talk focuses on experimental and mathematical approaches to understand two types of interactions in Pseudomonas bacteria: Quorum sensing, a mechanism of cell-cell communication that coordinates other cooperative behaviors, and iron acquisition via diffusible siderophores as both a cooperative and competitive behavior within and between species.

Link and Passcode : https://tum-conf.zoom.us/j/96536097137 , Code 101816

### 12.07.2021 15:00 Shuang Chen:Instability of small-amplitude periodic waves from fold-Hopf bifurcationvia ZOOM (Boltzmannstr. 3, 85748 Garching)

In this talk, I shall show our recent work on the existence and stability of small-amplitude periodic waves emerging from fold-Hopf equilibria in a system of one reaction-diffusion equation coupled with one ordinary differential equation. This coupled system includes the FitzHugh-Nagumo system, caricature calcium models, consumer-resource models and other models in the real-world applications. Based on the recent results on the averaging theory, we solve periodic solutions in related three-dimensional systems and then prove the existence of periodic waves arising from fold-Hopf bifurcations. After analyzing the linearization about periodic waves by the relatively bounded perturbation, we prove the instability of small-amplitude periodic waves through a perturbation of the unstable spectra for the linearizations about the fold-Hopf equilibria.

### 14.07.2021 13:00 Björn de Rijk, Universität Stuttgart :Stability of Pattern-Forming Fronts with a Quenching Mechanism via ZOOM (Boltzmannstr. 3, 85748 Garching)

The onset of pattern formation, where a localized perturbation of a destabilized ground state leads to an invading front leaving periodic patterns in its wake, is well-understood. In spatially homogeneous systems such pattern-forming fronts are unstable as any perturbation ahead of the front grows exponentially in time due to the instability of the ground state. Nevertheless, pattern-forming fronts are observed in various spatially inhomogeneous settings such as light-sensing reaction-diffusion systems, directional solidification of crystals or ion beam milling. In these settings the unstable state is only established in the wake of the heterogeneity after which patterns start to nucleate. Consequently, perturbations cannot grow far ahead of the interface of the pattern-forming front. This begs the question of whether stability can be rigorously established. In this talk, I answer this question affirmative by presenting a stability result for pattern-forming fronts against $L^2$-perturbations in the spatially inhomogeneous complex Ginzburg-Landau equation. A technical challenge is posed by the presence of unstable absolute spectrum which prohibits the use of standard tools such as exponential dichotomies. Instead, we projectivize the linear flow and study the associated matrix Riccati equation on the Grassmannian manifold. Eigenvalues can then be identified as the roots of the meromorphic Riccati-Evans function. This is joint work with Ryan Goh (Boston University).

Link and Passcode : https://tum-conf.zoom.us/j/96536097137 , Code 101816

### 19.07.2021 15:00 Yunan Yang, Ph.D.:Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant MeasuresVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

Parameter identification determines the essential system parameters required to build real-world dynamical systems by fusing crucial physical relationships and experimental data. However, the data-driven approach faces many difficulties, such as discontinuous or inconsistent time trajectories and noisy measurements. The ill-posedness of the inverse problem comes from the chaotic divergence of the forward dynamics. Motivated by the challenges, we shift from the Lagrangian particle perspective to the state space flow eld's Eulerian description. Instead of using pure time trajectories as the inference data, we treat statistics accumulated from the Direct Numerical Simulation (DNS) as the observable. The continuous analog of the latter is the physical invariant probability measure, a distributional solution of the stationary continuity equation. Thus, we reformulate the original parameter identification problem as a data-fitting, PDE-constrained optimization problem.

### 19.07.2021 16:00 Dr Jemima M. Tabeart :Parallelisable preconditioners for saddle point weak-constraint 4D-VarVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

The saddle point formulation of weak-constraint 4D-Var offers the possibility of exploiting modern computer architectures. Developing good preconditioners which retain the highly-parallelisable nature of the saddle point system has been an area of recent research interest, especially for applications to numerical weather prediction. In this presentation I will present new proposals for preconditioners for the model and observation error covariance terms which explicitly incorporate model information and correlated observation error information respectively for the first time. I will present theoretical results comparing our new preconditioners to existing standard choices of preconditioners for both the block diagonal and inexact constraint forms. Finally I will present two numerical experiments for the heat equation and Lorenz 96 and show that even when our theoretical assumptions are not completely satisfied, our new preconditioners lead to improvements in the inexact constraint setting

### 19.07.2021 16:00 David Geldbach (LMU; MSc presentation):Ergodicity of a dynamical XY-model(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

We consider the XY-model, a model for continuous spins on the d-dimensional Euclidean lattice, and discuss a time evolution for this model. In this time evolution, every spin behaves like a Brownian motion drifting to a local minimum of the Hamiltonian. If the underlying lattice is one-dimensional or if the temperature is high (for d>1), then the process converges to the unique Gibbs measure in a uniform sense. This is proven by showing a logarithmic Sobolev inequality for the Gibbs measure.

### 26.07.2021 10:15 Jacob Leygonie (University of Oxford):The fiber of Persistent Homology for Simplicial ComplexesOnline (Boltzmannstr. 3, 85748 Garching)

We study the inverse problem for persistent homology: For a fixed simplicial complex, we analyse the fiber of the continuous map PH on the space of filters that assigns to a filter the barcode of its associated sublevel set filtration. We find that PH is best understood as a map of stratified spaces. Over each stratum of the barcode space the map PH restricts to a fiber bundle with fiber a polyhedral complex. We illustrate the theory on the example of the triangle, which is rich enough to have a Möbius band as one of its fibers.