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DTSTART;TZID=America/Los_Angeles:20260413T161500
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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:20260414T121500
DTEND;TZID=America/Los_Angeles:20260414T131000
DTSTAMP:20260419T141144
CREATED:20260123T051413Z
LAST-MODIFIED:20260407T032128Z
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SUMMARY:Knot complements\, series invariants and Lie superalgebra (John Yoonseok Chae)
DESCRIPTION:Inspired by the categorification program for a numerical invariant of three-manifolds\, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the series invariant of the former case to Lie superalgebras. It was recently generalized to knot complements. In this talk\, we review the original series invariants and introduce the recent generalization and explore its properties and examples.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-helen-wong-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20260417T110000
DTEND;TZID=America/Los_Angeles:20260417T121500
DTSTAMP:20260419T141144
CREATED:20260110T235143Z
LAST-MODIFIED:20260416T002939Z
UID:3956-1776423600-1776428100@colleges.claremont.edu
SUMMARY:CCMS Colloquium: Ryan Moruzzi (CSU Northridge)
DESCRIPTION:CCMS Colloquium invites you to a talk by Ryan Moruzzi (CSU Northridge)\n\n \nTitle:  Exploring Leaky Forcing Through Hopi Rectangle graphs\n \nAbstract:  Leaky forcing\, introduced in 2019\, is a graph-coloring process motivated by questions of network monitoring\, in which the loss of information can hinder propagation through a graph. As a variant of standard zero forcing\, leaky forcing has opened new directions in the study of zero forcing and related graph parameters. In this talk\, based on joint work with students\, we will collaboratively investigate the leaky forcing number for several graphs before focusing on a family of graphs called Hopi Rectangles. By viewing these graphs as induced subgraphs of d-dimensional grid graphs\, we classify their leaky forcing numbers. Time permitting\, we will conclude by discussing the maximum nullity of this graph family and its connection to standard zero forcing.\n \nBio: I am a husband\, father\, sports enthusiast\, and mathematician who enjoys spending time with my family and the energy of sports. I earned my B.S. in Mathematics from Cal Poly Pomona and my Ph.D. in Mathematics from the University of California\, Riverside\, where I specialized in representation theory. My research interests lie in combinatorics\, discrete mathematics\, and linear algebra\, with particular emphasis on the inverse eigenvalue problem of a graph\, zero forcing and its variations\, throttling\, and propagation time on graphs. I also care deeply about teaching and mentorship\, and as an educator I am committed to fostering equity and inclusion by working intentionally to remove barriers that limit student success.
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-6/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Sam Nelson":MAILTO:snelson@cmc.edu
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