Dr. Erik Bollt
Clarkson University
Will present a talk titled:
On Integrability as Matching Dynamical Systems through Koopman OperatorEigenfunctions
Abstract: Matching dynamical systems, that is changing coordinates to something simple, is at the heart of the study and classification of nonlinear dynamic behavior. In this presentation we use the Koopman operator and its spectrum for this endeavor. The Koopman operator has a long theoretical tradition but it has recently become extremely popular through data-driven methods such as dynamic mode decomposition (DMD) and variants, for applied problems such as coherence and also in control theory. We demonstrate through illustrative examples and machine learning methods that we can extend Koopman spectral theoretical and computational machinery beyond modeling and prediction, towards a systematic discovery of rectifying integrability coordinate transformations.
Date: November 22, 2024
Location: Snell 212
Time: 11:00am
ZOOM Link for virtual attendance:
https://clarkson.zoom.us/j/93541691606?pwd=cggjBnvRrYbr7mPOCqmmThM0lOOzOd.1
You can access this link by going to the Virtual Class & Recordings tab in Moodle.
Bio: Erik Bollt received PhD from the University of Colorado, Boulder. He is a Full Professor at Clarkson University and endowed as the W. Jon Harrington Professor of Mathematics with a joint appointment to Electrical and Computer Engineering, ECE. He serves as Director of C 3 S 2 the Clarkson Center for Complex Systems Science. Professor Bollt specializes in dynamical systems, chaos theory and turbulence, including as informed by data and signal processing, and remote sensing of the world’s oceans, as well as inverse problems in data processing, machine learning, and information theoretic questions for information flow and systems inference. Prof. Bollt published a book on these topics as applied to systems such as the Gulf of Mexico oil spill, (Applied and Computational Measurable Dynamics, Book Publisher: Society for Industrial and Applied Mathematics, (2013)).