## Dynamical Systems Seminars Spring 2019

The Dynamical Systems seminar is held on Monday afternoons at 4:00 PM in MCS 148. Tea beforehand is at 3:45 PM in MCS 144.

• February 4 No seminar

• February 11 Shugan Ji
Title: Time periodic solutions of nonlinear wave equation with x-dependent coefficients
Abstract: In this talk, we consider the time periodic solutions of nonlinear wave equation with x-dependent coefficients. Such a model arises from the forced vibrations of an inhomogeneous string and the propagation of seismic waves in nonisotropic media. We shall talk about some existence results on the time periodic solutions of such a model with different types of nonlinearity.

• February 18 No Seminar, President's Day

• February 25 Margaret Beck Boston University
Title: TBA
Abstract: TBA

• March 4 Michael Bialy (Tel Aviv University); Note: The tea and seminar will be held in MCS B33.
Title: Around Birkhoff's conjecture for convex and other billiards
Abstract: Birkhoff's conjecture states that the only integrable billiards in the plane are ellipses. I am going to give a survey of recent progress in this conjecture and to discuss geometric results and questions around it. Based on joint works with Andrey E. Mironov, Maxim Arnold. No prior knowledge of the subject will be assumed.
• March 11 No Seminar, Spring Break
• March 18 Jonathan Jacquette (Brandeis)
Title: Computer assisted proofs of Wright's and Jones' Conjectures: Counting and discounting slowly oscillating periodic solutions to a delay differential equation
Abstract: A classical example of a nonlinear delay differential equations is Wright's equation: $y'(t) = \alpha y(t-1) [1+y(t)]$, considering $\alpha >0$ and $y(t)>-1$. This talk discusses two conjectures associated with this equation: Wright's conjecture, which states that the origin is the global attractor for all $\alpha \in ( 0 , \pi /2 ]$; and Jones' conjecture, which states that there is a unique slowly oscillating periodic solution for $\alpha > \pi / 2$. To prove Wright's conjecture our approach relies on a careful investigation of the neighborhood of the Hopf bifurcation occurring at $\alpha = \pi /2$. Using a rigorous numerical integrator we characterize slowly oscillating periodic solutions and calculate their stability, proving Jones' conjecture for $\alpha \in [1.9,6.0]$ and thereby all $\alpha\geq 1.9$. We complete the proof of Jones conjecture using global optimization methods, extended to treat infinite dimensional problems.

• March 25 Matt Holzer (George Mason University)
Title: Invasion fronts in spatially extended systems
Abstract: Invasion fronts refer to fronts propagating into unstable states. An important characteristic of such fronts is the speed at which they propagate. In this talk, I will review wavespeed selection principles and discuss two recent research projects related to wavespeed selection. In the first, we study the emergence of locked fronts in a class of two component reaction diffusion equations. In the second, a model of global epidemics is considered and predictions for arrival times are obtained based upon the linearization about the unstable steady state.

• April 1 Diana Atanasova (Boston University)
Title: TBA
Abstract: TBA

• April 8 Cynthia A. Bradham (Boston University)
Title: TBA
Abstract: TBA
• April 15 No Seminar Patriot's Day
Title: TBA
Abstract: TBA
• April 22 Luigi Chierchia (University of Roma Tre)
Title: TBA
Abstract: TBA
• April 29 Bastian Hilder (Universität Stuttgart)
Title: TBA
Abstract: TBA
Please also consider attending the Brown/BU/UMassAmherst seminar in PDE and Dynamics on May 3rd.