Applied/ACMS
Applied and Computational Mathematics Seminar
- When: Fridays at 2:25pm (except as otherwise indicated)
- Where: 901 Van Vleck Hall
- Organizers: Maurice Fabien, Chris Rycroft, and Saverio Spagnolie,
- To join the ACMS mailing list: Send mail to acms+join@g-groups.wisc.edu.
Fall 2023
| date | speaker | title | host(s) |
|---|---|---|---|
| Sep 8 | Erik Bollt (Clarkson University) | A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions | Chen |
| Sep 15 | John Schotland (Yale University) | Li | |
| Sep 22 | Balazs Boros (U Vienna) | Craciun | |
| Sep 29 | Peter Jan van Leeuwen (Colorado State University) | Chen | |
| Wed Oct 4 | Edriss Titi (Cambridge/Texas A&M) | Distringuished Lecture Series | Smith, Stechmann |
| Oct 6 | No Friday seminar | Distinguished lecture this week on Wednesday | |
| Oct 13 | Da Yang (University of Chicago) | Smith | |
| Oct 20 | Yuehaw Khoo (University of Chicago) | Li | |
| Oct 27 | Shukai Du (UW) | Stechmann | |
| Nov 3 | Lise-Marie Imbert-Gérard (University of Arizona) | Rycroft | |
| Nov 10 | Timothy Atherton (Tufts) | Chandler, Spagnolie | |
| Nov 17 | Daphne Klotsa | Rycroft | |
| Nov 24 | Thanksgiving break | ||
| Dec 1 | |||
| Dec 8 | |||
| Pending | Invite sent to Talea Mayo | Fabien |
Abstracts
Erik Bollt (Clarkson University)
A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions
Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of non- linear dynamic behavior (e.g. through normal forms). In this presentation we will argue that the use of the Koopman operator and its spectrum are particularly well suited for this endeavor, both in theory, but also especially in view of recent data-driven machine learning algorithmic developments. Recall that the Koopman operator describes the dynamics of observation functions along a flow or map, and it is formally the adjoint of the Frobenius-Perrron operator that describes evolution of densities of ensembles of initial conditions. The Koopman operator has a long theoretical tradition but it has recently become extremely popular through numerical 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 that we can nontrivially extend the applicability of the Koopman spectral theoretical and computational machinery beyond modeling and prediction, towards a systematic discovery of rectifying integrability coordinate transformations.
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