Current Series

[View Past Series]

Tue Sep 15

Dynamical Systems

2:30pm - Zoom - see link below
Dynamical systems for metabolic networks
Nicola Vassena, Free University Berlin

In this talk I will give an overview of one approach to the analysis of metabolic networks, using dynamical systems. When considered in applications, one of the main features of these networks is that the interaction functions (reaction rates) are practically unknown. That is, the most reliable data is the structure of network. For this reason, we present here a qualitative approach based on the structure of the network, only, where no quantitative information is needed. In particular, following this approach, we introduce how to address some bifurcation problems and sensitivity analysis.

https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Sep 22

Dynamical Systems

2:30pm - Zoom - see link below
Anderson localization for disordered trees
Selim Sukhtaiev, Auburn University

In this talk, we will discuss a mathematical treatment of a disordered system modeling localization of quantum waves in random media. We will show that the transport properties of several natural Hamiltonians on metric and discrete trees with random branching numbers are suppressed by disorder. This phenomenon is called Anderson localization.

https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Oct 06

Dynamical Systems

2:30pm - Zoom link: See abstract
Epidemiological Forecasting with Simple Nonlinear Models
 Joceline Lega , University of Arizona

Every week, the CDC posts COVID-19 death forecasts for the US and its states and territories. These estimates are created with an ensemble model that combines probabilistic predictions made by a variety of groups in the US and abroad. Our model, EpiCovDA, which is developed by mathematics graduate student Hannah Biegel and combines simple nonlinear modeling with data assimilation, is one of these contributions. In this talk, I will present a novel paradigm for epidemiological modeling that is based on a dynamical systems perspective, and which consists in describing an outbreak in terms of incidence versus cumulative case curves. I will then explain how this approach may be used for parameter estimation and how it is combined with data assimilation in EpiCovDA. Zoom Link: https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Oct 13

Dynamical Systems

2:30pm - Zoom link: See abstract
A coordinate transformation to highlight interesting flow features: local orthogonal rectification
Jonathan Rubin, University of Pittsburgh

Following some pioneering earlier work, there has been an uptick in efforts to develop coordinate transformations that provide natural coordinate systems in which it becomes easier to study certain flow features. Many of these transformations are local or focus on periodic orbits and associated small perturbations. In this talk, I will introduce a new coordinate transformation, local orthogonal rectification (LOR), recently developed by my graduate student Ben Letson (SFL Scientific) and me. I will illustrate how LOR provides new insights about forms of transient dynamics including rivers, dynamics of trajectories as they approach periodic orbits, and canards, and represents a useful tool that others may wish to apply for the analysis of such phenomena.

Zoom Link: https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Oct 20

Dynamical Systems

10:00am - Zoom Link - See Abstract
Nonlinear stability of fast invading fronts in a Ginzburg-Landau equation with an additional conservation law
 Bastian Hilder , University of Stuttgart  

In this talk, I consider the stability of traveling fronts connecting an invading state to an unstable ground state in a Ginzburg-Landau equation with an additional conservation law. This system appears generically as an amplitude equation for Turing pattern forming systems admitting a conservation law structure such as the Bénard-Marangoni convection problem. The main result is the nonlinear stability of sufficiently fast fronts with respect to perturbations which are exponentially localized ahead of the front. The proof is based on the use of exponential weights ahead of the front to stabilize the ground state. After presenting the general strategy, I discuss the specific challenges faced in the proof, namely the lack of a comparison principle and the fact that the invading state is only diffusively stable, i.e. perturbations of the invading state decay polynomially in time.

Zoom Link: https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Oct 27

Dynamical Systems

2:30pm - Via Zoom Link - see abstract
Dynamics on networks (and other things!)
Lee DeVille, University of Illinois

We will introduce several models connected to applications and present several results, mostly analytic but also some numerical.  These models will be defined on networks or higher-order objects (e.g. simplicial complexes).  In many of the cases, the dynamical systems can be characterized as “nonlinear Laplacians”; as such, various classical and not-so-classical results about Laplacians will be the secret sauce that undergirds the results.   We will also try to give some insight into the applications that give rise to the problems, as time permits.

Zoom Link: https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-