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## Joint Dynamics and PDE Seminar

The Boston University Department of Mathematics and Statistics, Brown University's Department of Mathematics and Division of Applied Mathematics, and the University of Massachusetts Amherst Department of Mathematics and Statistics hold joint seminars on topics in dynamics and PDE. The schedule and locations for these events can be found below. For a list of all past events of the seminar please visit the BU/Brown/UMass PDE Seminar Archive.

The Brown/BU/UMass Seminars are  currently organized by

The next seminar will take place at Boston University on April 27th 2022 (Wednesday). More details will follow.

### Spring 2022

Gigliola Staffilani (MIT)

Abstract: In the last two decades great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a collection of techniques: Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of results using as model problem mainly the periodic 2D cubic nonlinear Schrodinger equation.

Aric Wheeler (Indiana University)

Abstract: Generalizing results of Matthews-Cox/Sukhtayev for a model reaction-diffusion equation, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation in the presence of conservation laws. In the nonconvective, reaction-diffusion case, this is seen similarly as in Matthews-Cox, Sukhtayev to be a real Ginsburg-Landau equation weakly coupled with a diffusion equation in a large-scale mean-mode vector comprising variables associated with conservation laws.

Anastassiya Semenova (ICERM, Brown)
Zachary William Bezemek (BU)
Dominic Skinner (MIT)

Abstract: Living systems maintain or increase local order by working against the second law of thermodynamics. Thermodynamic consistency is restored as they consume free energy, thereby increasing the net entropy of their environment. Recently introduced estimators for the entropy production rate have provided major insights into the efficiency of important cellular processes. In experiments, however, many degrees of freedom typically remain hidden to the observer, and, in these cases, existing methods are not optimal.

Constantin Arnscheidt (MIT)

Abstract: Recent work on dynamical systems has highlighted the possibility of "rate-induced tipping", in which a system undergoes an abrupt transition when a perturbation exceeds a critical rate of change. Here we argue that rate-induced tipping towards extinction is likely a ubiquitous feature of evolutionary systems. We demonstrate the emergence of rate-induced extinction in two general evolutionary-ecological models, and connect these results with the established literature on "evolutionary rescue" as well as recent work on mass extinctions.

Paul Blochas (University of Rennes 1)

Abstract: In this talk, I will present a result obtained in a recent paper about the study of the stability in time of a family $(\underline{U}_\epsilon)_{0 < \epsilon < \epsilon_0}$ of traveling waves solutions to \begin{align*} \partial_t u+\partial_x(f(u))=g(u)+\epsilon \partial_x^2u \end{align*} that approximate a given Riemann shock, and we aim at showing some uniform asymptotic orbital stability result of these waves under some conditions that guarantee the asympotic orbital stability of the corresponding Riemann shock, as proved in a previous work of V.