Calendar

Posted November 11, 2024

Colloquium Questions or comments?

Benjamin Dodson, Johns Hopkins University
Global well-posedness and scattering for the radial, conformal wave equation

In this talk we prove global well-posedness and scattering for the radially symmetric nonlinear wave equation with conformally invariant nonlinearity. We prove this result for sharp initial data.

Posted August 21, 2024
Last modified November 10, 2024

Control and Optimization Seminar Questions or comments?

Benedetto Piccoli, Rutgers University, Camden AMS Fellow, SIAM W. T. and Idalia Reid Prize Awardee
Control Theory in Traffic Applications: 100 Years of Traffic Models

In 1924, in The Quarterly Journal of Economics, Frank H. Knight debated on social costs using an example of two roads, which was the basis of Wardrop’s principle. The author suggested the use of road tolls, and it was probably the first traffic model ever. A few other milestones of a long history include the traffic measurements by Greenshields in 1934, the Lighthill-Whitham-Richards model in the late 1950s, and follow-the-leader microscopic models. After describing some of these milestones, we will turn to the modern theory of conservation laws on topological graphs with applications to traffic monitoring. The theory requires advanced mathematics, such as BV spaces and Finsler-type metrics on L1. In the late 2000s, this theory was combined with Kalman filtering to deal with traffic monitoring using data from cell phones and other devices. Then we will turn to measure-theoretic approaches for multi-agent systems, which encompass follow-the-leader-type models. Tools from optimal transport allow us to deal with the mean-field limit of controlled equations, representing the action of autonomous vehicles. We will conclude by discussing how autonomy can dissipate traffic waves and reduce fuel consumption, and we will illustrate results of a 2022 experiment with 100 autonomous vehicles on an open highway in Nashville.