Seminars in Dynamics
Dynamical Systems Seminars
The Dynamical Systems seminar is held on Monday afternoon at
4:00 PM in MCS 148. Tea beforehand at 3:45 PM in MCS 153.
- January 27: Kelly McQuighan (Brown)
Title: Oscillons near Hopf Bifurcations of Planar Reaction Diffusion Equations
Abstract: Oscillons are spatially localized, temporally oscillating, radially
symmetric structures. They have been observed in various experimental
contexts, including fluid systems, granular systems, and chemical
systems. Oscillons often arise near forced Hopf bifurcations, which are
modeled mathematically with the forced complex Ginzburg-Landau equation. I
present a proof of the existence of small amplitude oscillons in the planar
forced complex Ginzburg-Landau equation through a geometric blow-up
analysis. The analysis in complemented by a numerical continuation study of
oscillons away from onset using Matlab and AUTO. This is joint work with Bjorn
Sandstede at Brown University.
- February 3: Jiayin Jin
Title: The dynamics of boundary droplets for the mass-conserving Allen-Cahn
Abstract: We establish the existence of a global invariant manifold of bubble states for
the mass-conserving Allen-Cahn Equation in two space dimensions and give the dynamics
for the center of the bubble.
- February 10: Greg Faye (Minnesota)
Title: Existence of traveling pulse solutions in excitable media with nonlocal
Abstract: In this talk, we prove the existence of fast traveling pulses for a
class of FitzHugh-Nagumo equations with nonlocal diffusion. Unlike the
dynamical systems approach via geometric singular perturbation theory
(Fenichel's theorem and Exchange Lemma), our proof relies on matched
asymptotics techniques and Fredholm properties of differential operators on
suitable Banach spaces (Spectral Flow and Nonlocal Exchange Lemma). This is
joint work this Arnd Scheel.
- February 17: No seminar - President's Day
- February 24: Mei Yin (Brown)
Title: Phase transitions in the edge-triangle exponential random graph model
Abstract: The edge-triangle exponential random graph model has been a topic of continued research interest. We review recent developments in the study of this classic model and concentrate on the phenomenon of phase transitions. We first describe the asymptotic feature of the model along general straight lines. We show that as we continuously vary the slopes of these lines, a typical graph
exhibits quantized behavior, jumping from one complete multipartite structure to another, and the jumps happen precisely at the normal lines of an infinite polytope. We then turn to exponential models where certain constraints are imposed and capture another interesting type of jump discontinuity. This expository talk is based on recent joint work with Alessandro Rinaldo and Sukhada Fadnavis and current joint work in progress with Richard Kenyon. We will point out that many questions/issues raised in this talk are actually studied under different names or from different directions in dynamics.
- March 3: Professional development session on research journals for
- March 10: No seminar - Spring Break
- March 17: Johanna
- March 24: No seminar.
- March 31: Ava Mauro
- April 7: Rocio Gonzalez Ramirez
- April 14: No seminar.
- April 18 (special Friday seminar): Sarah Koch (Michigan)
- April 21: No seminar - Patriot's Day
- April 28: Miles Wheeler (Brown)
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