The Dynamical Systems seminar is held on Monday afternoons at
4:00 PM in MCS B31 . There will be a brief tea in MCS B24 at 3:45PM. -->
September 12 Fall Social Event
All are welcome to come! Light refreshments will be provided.
September 19 Patrick Flynn
Title: The scattering problem for Vlasov-Poisson
Abstract: The Vlasov-Poisson system is a kinetic model for a
continuous density of particles interacting through either Newtonian
or Coulombic gravitation. I will describe the scattering problem for
this equation, where one must find the asymptotic dynamic as time goes
to infinity, and then connect the asymptotic behavior of the solution
at time minus infinity to time plus infinity through the so-called
scattering map. This model exhibits "modified" scattering, where the
asymptotic dynamic is given by the linearized equation, plus an
explicit nonlinear correction. To solve the scattering problem, we
apply the pseudo-conformal transformation, more widely used in the
study of the nonlinear Schrodinger equation. This transformation,
which inverts time, allows us to reformulate the scattering problem as
a Cauchy problem, which we then solve using Picard iteration. This
talk is based on joint work with Benoit Pausader, Zhimeng Ouyang, and
September 26 Bengier Ülgen Kılıç
Title: Thresholding and multi-body interactions orient cascades in spatially embedded networks
Abstract: PDF here!
October 3rd Natasa Dragovic
Title: The Perils Of Political Centrism
Abstract: In this talk I will present a model of two competing political candidates who shift views opportunistically to maximize their share of the vote. We start with some observations about the model. First, the best strategy for a candidate is often to move towards the other candidate, eventually resulting in two centrists with coalescing views. Second, this strategy ceases to be optimal as soon as sufficiently many voters respond to their candidate’s opportunistic drift towards the center by staying away from the polls altogether. The surprise is that the change in the optimal candidate position can, in certain circumstances, be discontinuous. The underlying mathematical mechanism is a blue-sky bifurcation.
This is a joint work with Bruce Boghosian, Christoph Börgers and Anna Haensch.