General-relativistic hydrogen and hydrogenic ions
Ebru Toprak (Yale University)
In this talk, I will speak how the static non-linear electromagnetic-vacuum spacetime of a point nucleus with negative bare mass affects the self-adjointness of the general relativistic Dirac Hamiltonian for a test electron, without and with an anomalous magnetic moment.
Snaking of contact defects in the Brusselator
Tim Roberts (Brown University)
The Brusselator is one of the oldest systems studied in spatial dynamics, first conceived as a result of Turing’s landmark work on the formation of stripe patterns in the 1960’s. Despite the decades and myriad studies since then, it remains a system of interest due to its ability to display a zoo of different complex behaviors. In this work we look at a newly discovered behavior, snaking of contact defects. Numerical studies by Tzou et al.
Stochastic collective behaviors in large neural networks
Jonathan Touboul (Brandeis University)
Spectral stability via the Maslov index and validated numerics
Hannah Pieper (Boston University)
Results from Sturm-Liouville theory tell us that the number of unstable eigenvalues of a scalar, second order linear operator coincides with the number of zeros of the eigenfunction associated to the zero eigenvalue. Recently, these results have been extended to a more general setting using the Maslov index, which allows for the spectral stability of nonlinear waves to be determined by counting so-called conjugate points.
The perils of political centrism
Natasa Dragovic (Tufts University)
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.
Riemannian interpretation of stochastic eigenvalue processes
Ching-Peng Huang (Brown University)
We show that the classical result of Dyson Brownian motion is a consequence of Riemannian submersion and systematically prove the same for other two eigenvalue processes, where the repulsive deterministic terms come from mean curvature flows as a gradient flow maximizing the volume of group orbits. The result is valid for the classical ensembles as well as general β-ensembles first realized in matrix models by Dimitriu and Edelman.
