## Seminar Categories

## Current Series

Tue Oct 01 |
## Dynamical Systems2:30pm - Vincent Hall 209Relative equilibrium configurations of gravitationally interacting rigid bodies Rick Moeckel, University of Minnesota Consider a collection of n rigid, massive bodies interacting according to their mutual gravitational attraction. A relative equilibrium motion is one where the entire configuration rotates rigidly and uniformly about a fixed axis all of the bodies are phase locked. Such a motion is possible only for special positions and orientations of the bodies. A minimal energy motion is one which has the minimum possible energy in its fixed angular momentum level. While every minimal energy motion is a relative equilibrium motion, the main result here is that a relative equilibrium motion of n >= 3 disjoint rigid bodies is never an energy minimizer. Since energy minimizers are the expected final states produced by tidal interactions, phase locking of 3 or more bodies will not occur. |

Tue Oct 15 |
## Dynamical Systems2:30pm - Vincent Hall 209Forecasting U.S. elections with compartmental models of infection Alexandria Volkening, Northwestern University U.S. election forecasting involves polling likely voters, making assumptions about voter turnout, and accounting for various features such as state demographics and voting history. While political elections in the United States are decided at the state level, errors in forecasting are correlated between states. With the goal of shedding light on the forecasting process and exploring how states influence each other, we develop a framework for forecasting elections in the U.S. from the perspective of dynamical systems. Through a simple approach that borrows ideas from epidemiology, we show how to combine a compartmental model with public polling data from HuffPost and RealClearPolitics to forecast gubernatorial, senatorial, and presidential elections at the state level. Our results for the 2012 and 2016 U.S. races are largely in agreement with those of popular pollsters, and we use our new model to explore how subjective choices about uncertainty impact results. We conclude by comparing our forecasts for the senatorial and gubernatorial races in the U.S. midterm elections of 6 November 2018 with those of popular pollsters. This is joint work with Daniel Linder (Augusta Univ.), Mason Porter (UCLA), and Grzegorz Rempala (Ohio State Univ.) |

Fri Nov 15 |
## Dynamical Systems2:30pm - Vincent Hall 20The mathematics of taffy pulling Jean-Luc Thiffeault, University of Wisconsin Taffy is a type of candy made by repeated 'pulling' (stretching andfolding) a mass of heated sugar. The purpose of pulling is to get air |

Tue Feb 04 |
## Dynamical Systems2:30pm - Vincent Hall 213Spectral Stability, the Maslov Index, and Spatial Dynamics Margaret Beck, Boston University Understanding the spectral stability of solutions to partial differential equations is an important step in predicting long-time dynamics. Recently, it has been shown that a topological invariant known as the Maslov Index can play an important role in determining spectral stability for systems that have a symplectic structure. In addition, related ideas have lead to a suggested generalization of the notion of spatial dynamics to general, multidimensional spatial domains. In this talk, the notions of spectral stability, the Maslov Index, and spatial dynamics will be introduced and an overview of recent results will be given. |

Tue Feb 25 |
## Dynamical Systems2:30pm - Vincent Hall 213Hyperbolic scattering in the N-body problem Rick Moeckel, University of Minnesota It is a classical result that in the N-body problem with positive energy, all solutions are unbounded in both forward and backward time. If all of the mutual distances between the particles tend to infinity with nonzero speed, the solution in called purely hyperbolic. In this case there is a well-defined asymptotic shape of the configuration of N points. We consider the scattering problem for solutions which are purely hyperbolic in both forward and backward time: given an initial shape at time minus infinity, which final shapes at time plus infinity can be reached via purely hyperbolic motions ? I will describe some recent work on this problem using a variation on McGehee's blow-up technique. After a change of coordinates and timescale we obtain a well-defined limiting flow at infinity and use it to get Chazy-type asymptotic estimates on the positions of the bodies and to study scattering solutions near infinity. This is joint work with G. Yu, R. Montgomery and N. Duignan. |