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Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients. | Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients. | ||
[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)Oscillatory mass-action systems | |||
Oscillatory mass-action systems | |||
Mass-action differential equations are probably the most common mathematical models in biochemistry, cell biology, and population dynamics. Since oscillatory behavior is ubiquitous in nature, there are several papers (starting with Alfred Lotka) that deal with showing the existence of periodic solutions in mass-action systems. The standard way of proving the existence of a limit cycle in a high-dimensional system is via Andronov-Hopf bifurcation. In this talk, we recall some specific oscillatory models (like glycolysis or phosphorylation), as well as more recent results that aim to systematically classify small mass-action reaction networks that admit an Andronov-Hopf bifurcation. | Mass-action differential equations are probably the most common mathematical models in biochemistry, cell biology, and population dynamics. Since oscillatory behavior is ubiquitous in nature, there are several papers (starting with Alfred Lotka) that deal with showing the existence of periodic solutions in mass-action systems. The standard way of proving the existence of a limit cycle in a high-dimensional system is via Andronov-Hopf bifurcation. In this talk, we recall some specific oscillatory models (like glycolysis or phosphorylation), as well as more recent results that aim to systematically classify small mass-action reaction networks that admit an Andronov-Hopf bifurcation. | ||
Revision as of 21:44, 18 September 2023
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 4:00pm B239 | John Schotland (Yale University) | Nonlocal PDEs and Quantum Optics | Li |
| Sep 22 | Balazs Boros (U Vienna) | Oscillatory mass-action systems | Craciun |
| Sep 29 | Peter Jan van Leeuwen (Colorado State University) | Nonlinear Causal Discovery, with applications to atmospheric science | 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 | Adam Stinchcombe (University of Toronto) | Cochran | |
| 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.
John Schotland (Yale University)
Nonlocal PDEs and Quantum Optics
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.
Balazs Boros (U Vienna)Oscillatory mass-action systems
Mass-action differential equations are probably the most common mathematical models in biochemistry, cell biology, and population dynamics. Since oscillatory behavior is ubiquitous in nature, there are several papers (starting with Alfred Lotka) that deal with showing the existence of periodic solutions in mass-action systems. The standard way of proving the existence of a limit cycle in a high-dimensional system is via Andronov-Hopf bifurcation. In this talk, we recall some specific oscillatory models (like glycolysis or phosphorylation), as well as more recent results that aim to systematically classify small mass-action reaction networks that admit an Andronov-Hopf bifurcation.
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