Seminar Categories

This page lists seminar series that have events scheduled between two months ago and twelve months from now and have speaker information available.

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-

Tue Nov 17

Dynamical Systems

2:30pm - Via Zoom See abstract
Dynamics of curved travelling fronts on a two-dimensional lattice
Mia Jukic, Leiden University

In this talk I will introduce the Allen-Cahn lattice differential equation (LDE) posed on a two dimensional lattice. It is a well-known result that this equation admits a traveling wave solution.  In the first part, I will explain the most interesting differences between the traveling waves arising from PDEs and the traveling waves arising from LDEs, such as dependence of the wave profile and the wave speed on the direction of propagation.  In the second part, I will present recent results on the  stability of the traveling wave solutions propagating in rational directions, and  show a connection between the solution of a discrete mean curvature flow with a drift term and the evolution of the interface region of a solution that starts as a bounded perturbation to the wave profile.Zoom Link: https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Jan 26

Dynamical Systems

12:20pm - See abstract for Zoom info
Bifurcations and patterns in the spatially extended Kuramoto model
Georgi Medvedev, Drexel University

The Kuramoto model (KM) describes the evolution of phase oscillators

rotating with random frequencies and interacting with each other through

nonlinear coupling. The spatially extended model  also includes a graph describing

the connectivity of the network. In the thermodynamic limit, the KM is approximated

by the Vlasov equation, a hyperbolic PDE describing the evolution of the probability

distribution of the oscillators in the phase space.

 

I will review the linear stability analysis of mixing, a steady state solution of the

Vlasov equation and will relate the bifurcations of mixing to spatiotemporal patterns

observed in the KM right after mixing loses stability. These patterns include stationary

and travelling clusters, twisted states, chimera states, and combinations of the above.

In contrast to reaction-diffusion systems, where patterns are expressed by smooth

solutions, they are served by tempered distributions for the model at hand.

 

I will also discuss the extension of these results to the KM with inertia,

which is used for modeling dynamics of power grids. This talk is based on the  joint work with

Hayato Chiba (Tohoku University) and Matthew Mizuhara (The College of New Jersey).

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Jan 26

Dynamical Systems

12:20pm - See abstract for Zoom info
Bifurcations and patterns in the spatially extended Kuramoto model
Georgi Medvedev, Drexel University

The Kuramoto model (KM) describes the evolution of phase oscillators

rotating with random frequencies and interacting with each other through

nonlinear coupling. The spatially extended model  also includes a graph describing

the connectivity of the network. In the thermodynamic limit, the KM is approximated

by the Vlasov equation, a hyperbolic PDE describing the evolution of the probability

distribution of the oscillators in the phase space.

 

I will review the linear stability analysis of mixing, a steady state solution of the

Vlasov equation and will relate the bifurcations of mixing to spatiotemporal patterns

observed in the KM right after mixing loses stability. These patterns include stationary

and travelling clusters, twisted states, chimera states, and combinations of the above.

In contrast to reaction-diffusion systems, where patterns are expressed by smooth

solutions, they are served by tempered distributions for the model at hand.

 

I will also discuss the extension of these results to the KM with inertia,

which is used for modeling dynamics of power grids. This talk is based on the  joint work with

Hayato Chiba (Tohoku University) and Matthew Mizuhara (The College of New Jersey).

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Feb 02

Dynamical Systems

12:20pm - See abstract for Zoom info
The effect of contact structure on hypergraph contagion models
Juan Restrepo, University of Colorado, Boulder

  In contrast to the traditional network paradigm, the dynamics of network social contagion processes are often mediated by interactions between multiple nodes. These interactions can profoundly modify the dynamics of contagion processes, resulting in bistability, hysteresis, and explosive transitions. We present a mean-field description of the dynamics of the SIS model on hypergraphs and use it to study the effect of heterogeneity on contagion dynamics. As an illustrative case, we focus on the example of a hypergraph where contagion is mediated by both links(pairwise interactions) and triangles (three-way interactions). We consider two different mechanisms of higher-order contagion and healing, and the cases where links and triangles connect preferentially to the same nodes or are chosen independently of each other. We find that explosive transitions can be suppressed by heterogeneity in the link degree distribution when links and triangles are chosen independently, or when link and triangle connections are positively correlated when compared to the uncorrelated case. In addition, we discuss the effect of assortative hypergraph structure on the contagion dynamics.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Feb 02

Dynamical Systems

12:20pm - See abstract for Zoom info
The effect of contact structure on hypergraph contagion models
Juan Restrepo, University of Colorado, Boulder

  In contrast to the traditional network paradigm, the dynamics of network social contagion processes are often mediated by interactions between multiple nodes. These interactions can profoundly modify the dynamics of contagion processes, resulting in bistability, hysteresis, and explosive transitions. We present a mean-field description of the dynamics of the SIS model on hypergraphs and use it to study the effect of heterogeneity on contagion dynamics. As an illustrative case, we focus on the example of a hypergraph where contagion is mediated by both links(pairwise interactions) and triangles (three-way interactions). We consider two different mechanisms of higher-order contagion and healing, and the cases where links and triangles connect preferentially to the same nodes or are chosen independently of each other. We find that explosive transitions can be suppressed by heterogeneity in the link degree distribution when links and triangles are chosen independently, or when link and triangle connections are positively correlated when compared to the uncorrelated case. In addition, we discuss the effect of assortative hypergraph structure on the contagion dynamics.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Feb 16

Dynamical Systems

12:20pm - via Zoom
Locked fronts in a discrete time discrete space population model
Matt Holzer, George Mason University

We study locked invasion fronts in a model of population dynamics where both space and time are taken to be discrete variables. Locked fronts propagate with rational speed and are observed to persist as system parameters are varied. We construct locked fronts for a particular piecewise linear reproduction function. These fronts are shown to be linear combinations of exponentially decaying solutions to the linear system near the unstable state. We derive conditions on system parameters for which locking occurs and compare our predictions to observations in direct numerical simulations. We obtain leading order expansions for the locking regions in the limit as the migration parameter tends to zero. Strict spectral stability in exponentially weighted spaces is also established.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Mar 02

Dynamical Systems

12:20pm - via Zoom
Synchronization of clocks and metronomes: A perturbation analysis based on multiple timescales
Alice Nadeau, Cornell University

In 1665, Huygens observed that two pendulum clocks hanging from the same board became synchronized in antiphase after hundreds of swings. On the other hand, modern experiments with metronomes placed on a movable platform show that they often tend to synchronize in phase, not antiphase. Here we study both in-phase and antiphase synchronization in a model of pendulum clocks and metronomes and analyze their long-term dynamics with the tools of perturbation theory.  Specifically, we exploit the separation of timescales between the fast oscillations of the individual pendulums and the much slower adjustments of their amplitudes and phases. By scaling the equations appropriately and applying the method of multiple timescales, we derive explicit formulas for the regimes in parameter space where either antiphase or in-phase synchronization are stable, or where both are stable. Although this sort of perturbative analysis is standard in other parts of nonlinear science, it has been applied surprisingly rarely in the context of Huygens's clocks. Unusual features of our approach include its treatment of the escapement mechanism, a small-angle approximation up to cubic order, and both a two- and three-timescale asymptotic analysis.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Mar 16

Dynamical Systems

12:20pm - via Zoom
Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
Maximilian Engel, Freie Universität Berlin

  We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted proof. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains and the modified Furstenberg-Khasminskii formula, the problem boils down to the rigorous computation of eigenfunctions of the Kolmogorov operators describing distributions of the underlying stochastic process. The proof techniques fall into the category of a posteriori validation methods, meaning that we first compute a numerical approximation of an eigenpair for the operators and then use a fixed point argument to prove the existence of an exact solution nearby obtaining explicit error bounds.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Mar 23

Dynamical Systems

12:20pm - via Zoom
The Continuation of Conley's Attractor-Repeller Pair Decomposition for Differential Inclusions
Cameron Thieme, University of Minnesota 

Over the past few decades, piecewise-continuous differential equations have become increasingly popular in scientific models.  In particular, conceptual climate models often take this form.  These nonsmooth systems are typically reframed as Filippov systems, a special type of multivalued differential inclusion.  The qualitative properties of these inclusions have been studied over the last few decades, primarily in the context of control systems.  Our interest in these systems is in understanding what behavior identified in the nonsmooth model may be continued to families of smooth differential equations which limit to the Filippov system; determining this information is particularly important in this context because the piecewise-continuous model is frequently considered to be a heuristically understandable approximation of a more realistic smooth system.  In this talk we will examine how Conley index theory may be applied to the study of differential inclusions in order to address this goal.  In particular, we will discuss how attractor-repeller pairs identified in a Filippov system continue to nearby smooth systems.Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Mar 30

Dynamical Systems

12:20pm - See abstract for Zoom info
Topological Data Analysis for Dynamic Data in Intracellular Transport
Veronica Ciocanel, Duke University

Actin filaments are polymers that interact with motor proteins inside cells and play important roles in cell motility, shape, and development. Depending on its function, this dynamic network of proteins reshapes and organizes in a variety of structures, including bundles, clusters, and contractile rings. Motivated by observations from the roundworm, we use an agent-based modeling framework to study interactions between filaments and motor proteins inside cells. We develop a method based on topological data analysis to understand time-series data extracted from these dynamical systems models of filament interactions. We use this technique to compare the filament organization resulting from motors with different properties. This approach also raises research questions about how to assess the significance of topological features in common topological summary visualizations, especially for data from dynamic simulations.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Apr 13

Dynamical Systems

12:20pm - See abstract for Zoom info
Multivariate Climate Projections: More Accurate Equilibrium Estimations & Evolution of Climate Feedbacks
Robbin Bastiaansen, Utrecht University

When the climate system is forced by e.g. changes in atmospheric CO2, it responds to this change on multiple time scales, showing responses on time scales ranging from very short to very long. It is clear that the behavior over these time scales can be very different: for instance, as ice melts, the ice-albedo feedback becomes less and less important. Predominantly used climate projection methods, however, typically do not adequately take such state changes into account and are univariate: they only consider the global mean surface temperature -- assuming everything else is just linearly correlated to that. In this talk, I will show multivariate estimation techniques that are capable of tracking these state changes by incorporating additional observables into the analysis directly. This has two important advantages. First, such methods are better equipped to provide projections for the longer time scales (for instance, estimations of equilibrium climate sensitivity). Second, it makes it possible to estimate other observables directly -- without making assumptions on their relation to the global mean surface temperature -- which leads to better quantitative insights in how precisely the climate will change in the future (for instance, how climate feedback processes might change over time).Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-

Tue Apr 27

Dynamical Systems

12:20pm - See abstract for Zoom info
A Dynamical Model for the Origin of Anisogamy
Joseph Johnson, University of Michigan 

The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon.  Unlike some prior work, we do not assume the existence of mating types.  We also model frequency dependent selection via “mean-field coupling,” whereby the likelihood that a gamete survives is an increasing function of its size relative to the population’s mean gamete size.  Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.

Zoom link (provide email address to receive link): https://umn.zoom.us/meeting/register/tJ0lc-CsrjIqHN1xLg-ljWWlDIYBIUwKwJK-