Posted November 11, 2024
Colloquium Questions or comments?
3:30 pm Lockett 232
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?
10:30 am – 11:20 am Zoom (click here to join)
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.
Posted October 29, 2024
Last modified October 30, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 233
Alexander V. Kiselev, University of Bath
Abstract TBA (topic in applied scattering/spectral theory)
(Host: Stephen Shipman)
Posted August 29, 2024
Algebra and Number Theory Seminar Questions or comments?
2:30 pm – 3:30 pm Lockett 233 or click here to attend on Zoom
Jiuya Wang, University of Georgia
TBA
Posted August 30, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Locket 233
Huong Vo, Louisiana State University
TBD
Posted August 13, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
Karl Johansson, KTH Royal Institute of Technology, Sweden
Fellow of IEEE, IEEE CSS Hendrik W. Bode Lecture Prize Awardee
TBA
Posted September 4, 2024
Control and Optimization Seminar Questions or comments?
10:30 am – 11:20 am Zoom (click here to join)
María Soledad Aronna, Escola de Matematica Aplicada, Brazil
TBA
Posted November 10, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Rushikesh Kamalapurkar, University of Florida
Operator Theoretic Methods for System Identification
Operator representations of dynamical systems on Banach spaces provide a wide array of modeling and analysis tools. In this talk, I will focus on dynamic mode decomposition (DMD). In particular, new results on provably convergent singular value decomposition (SVD) of total derivative operators corresponding to dynamic systems will be presented. In the SVD approach, dynamic systems are modeled as total derivative operators that operate on reproducing kernel Hilbert spaces (RKHSs). The resulting total derivative operators are shown to be compact provided the domain and the range RKHSs are selected carefully. Compactness is used to construct a novel sequence of finite rank operators that converges, in norm, to the total derivative operator. The finite rank operators are shown to admit SVDs that are easily computed given sample trajectories of the underlying dynamical system. Compactness is further exploited to show convergence of the singular values and the right and left singular functions of the finite rank operators to those of the total derivative operator. Finally, the convergent SVDs are utilized to construct estimates of the vector field that models the system. The estimated vector fields are shown to be provably convergent, uniformly on compact sets. Extensions to systems with control and to partially unknown systems are also discussed. This talk is based in part on joint works [RK23], [RK24], and [RRKJ24] with J.A. Rosenfeld.
Posted October 14, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Alexandru Hening, Texas A&M University
TBA
Posted November 1, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Ali Zemouche, University of Lorraine, France
TBA
Posted November 12, 2024
Geometry and Topology Seminar Seminar website
3:30 pm
Porter Morgan, University of Massachusetts Amherst
TBD
Posted November 12, 2024
Geometry and Topology Seminar Seminar website
3:30 pm
Dave Auckly, Kansas State University
TBD
Posted September 19, 2024
Last modified October 25, 2024
Colloquium Questions or comments?
3:30 pm Lockett 232
Bogdan Suceava, California State University Fullerton
TBD
Posted November 7, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Irena Lasiecka, University of Memphis
AACC Bellman Control Heritage Awardee, AMS Fellow, SIAM Fellow, and SIAM Reid Prize Awardee
TBA