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DTSTART;TZID=America/Los_Angeles:20260413T161500
DTEND;TZID=America/Los_Angeles:20260413T171500
DTSTAMP:20260509T171120
CREATED:20260320T224421Z
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UID:4058-1776096900-1776100500@colleges.claremont.edu
SUMMARY:Extremal Eigenvalues of Weighted Steklov Problems (Chiu-Yen Kao\, CMC)
DESCRIPTION:Abstract: We study the optimization of Steklov eigenvalues with respect to a boundary density function ρ on a bounded Lipschitz domain. We investigate the minimization and maximization of a Steklov eigenvalue over admissible densities satisfying pointwise bounds and a fixed integral constraint. We establish the existence of optimal solutions and provide structural characterizations: minimizers are bang-bang functions and may have disconnected support\, while maximizers are not necessarily bang-bang. On circular domains\, the minimization problem admits infinitely many minimizers generated by rotational symmetry\, while the maximization problem has infinitely many distinct maximizers that are not symmetry-induced. We also show that an eigenvalue is generally neither convex nor concave with respect to the density function\, limiting the use of classical convex optimization tools. To address these challenges\, we analyze the objective functional and introduce a Fréchet differentiable surrogate that enables the derivation of optimality conditions. We further design an efficient numerical algorithm\, with experiments illustrating the difficulty of recovering optimal densities when they lack smoothness or exhibit oscillations.
URL:https://colleges.claremont.edu/ccms/event/extremal-eigenvalues-of-weighted-steklov-problems-chiu-yen-kao-cmc/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
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DTSTART;TZID=America/Los_Angeles:20260420T161500
DTEND;TZID=America/Los_Angeles:20260420T171500
DTSTAMP:20260509T171120
CREATED:20260408T061621Z
LAST-MODIFIED:20260408T061621Z
UID:4067-1776701700-1776705300@colleges.claremont.edu
SUMMARY:The Secret Life of Turbulent Fluids (Vincent Martinez\, Caltech)
DESCRIPTION:Abstract: Turbulence influences our lives in a multitude of ways\, ranging from the mundane (when we stir milk into our coffee) to the spectacular (the formation of galaxies). It is a great achievement of the human intellect that we are able to locate fundamental mechanisms shared by phenomenon with such a dramatic difference in scale and subsequently study them abstractly through mathematics. This talk will present some of the ways for how fluids and turbulent motion can be studied mathematically and introduce a few interesting problems\, both theoretical and practical\, of ongoing scientific relevance.
URL:https://colleges.claremont.edu/ccms/event/the-secret-life-of-turbulent-fluids-vincent-martinez-caltech/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20260427T161500
DTEND;TZID=America/Los_Angeles:20260427T171500
DTSTAMP:20260509T171120
CREATED:20260424T155240Z
LAST-MODIFIED:20260424T155341Z
UID:4091-1777306500-1777310100@colleges.claremont.edu
SUMMARY:From ICON to GenICON: In-Context Operator Learning with Uncertainty Quantification (Siting Liu\, UCR)
DESCRIPTION:Abstract: I will introduce In-Context Operator Networks (ICON)\, a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at inference time\, without any weight updates. ICON acts as a few-shot learner across forward and inverse problems for ODEs\, PDEs\, and mean-field control. I will then present a probabilistic interpretation: under a random differential equation data model\, ICON implicitly computes the posterior predictive mean given the context\, linking operator learning to Bayesian inference. This motivates GenICON\, a generative variant that samples from the posterior predictive for principled uncertainty quantification\, yielding a unified Bayesian view of in-context operator learning.
URL:https://colleges.claremont.edu/ccms/event/from-icon-to-genicon-in-context-operator-learning-with-uncertainty-quantification-siting-liu-ucr/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
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