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DTSTART;TZID=America/Los_Angeles:20231030T161500
DTEND;TZID=America/Los_Angeles:20231030T173000
DTSTAMP:20260425T074359
CREATED:20231019T153510Z
LAST-MODIFIED:20231023T034142Z
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SUMMARY:Applied Math Seminar: Jeremy Brandman (DCS corporation)
DESCRIPTION:Title \nControl algorithms for unmanned underwater vehicles: new approaches based on Hamilton-Jacobi equations and reinforcement learning. \nAbstract \nUnmanned underwater vehicles (UUVs) are defined by their ability to operate without direct human intervention.  As a result\, UUVs are valuable for surveillance tasks\, especially in the presence of hazardous environmental conditions. Specific applications of UUVs include seafloor mapping\, mine detection\, and oil pipeline inspection. \nIn this talk\, we propose new algorithms for two aspects of UUV control: path planning and vehicle guidance.  Path planning identifies a vehicle trajectory\, based on anticipated environmental conditions\, that achieves desired mission objectives (e.g. obstacle avoidance\, minimization of energy consumption). Vehicle guidance responds to observed environmental conditions in order to maintain fidelity to the path selected by the path planner. \nThe first half of this talk considers a new approach to path planning based on solving Hamilton-Jacobi partial differential equations (PDE).  The starting point for this method is the observation that the vehicle’s minimum travel-time satisfies a time-independent Hamilton-Jacobi equation .  Numerical solutions to this PDE are efficiently computed using the fast sweeping method.  Our approach is validated through several examples for which optimal trajectories are derived using the calculus of variations. \nThe second half of this talk introduces a reinforcement learning framework for incorporating in situ ocean current measurements into the guidance system in an energetically optimal manner.  Scaling and symmetry considerations turn out to play an important role in the framework’s efficiency and robustness.  Numerical results demonstrate that the energetic cost of transits executed under the guidance of a trained agent approaches optimal performance.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-jeremy-brandman/
LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ami Radunskaya":MAILTO:aradunskaya@pomona.edu
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231031T121500
DTEND;TZID=America/Los_Angeles:20231031T131000
DTSTAMP:20260425T074359
CREATED:20230921T041133Z
LAST-MODIFIED:20231013T160601Z
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SUMMARY:On the spectra of syntactic structures (Isabella Senturia\, Yale University)
DESCRIPTION:We explore the application of spectral graph theory to the problem of characterizing linguistically-significant classes of tree structures. We focus on various classes of syntactically-defined tree graphs\, and show that the spectral properties of different matrix representations of these classes of trees provide insight into the linguistic properties that characterize these classes. More generally\, our goal is to provide another route to understanding the mathematical structure of natural language\, one that does not come from extensive definitions and rules defined via linguistic extrapolation\, but instead is extracted directly from computation on the syntactically-defined graphical structures.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-via-zoom-isabella-senturia-yale-university/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231031T150000
DTEND;TZID=America/Los_Angeles:20231031T160000
DTSTAMP:20260425T074359
CREATED:20230918T204526Z
LAST-MODIFIED:20231030T204415Z
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SUMMARY:Claremont Topology Seminar: Konstantinos Varvarezos (UCLA)
DESCRIPTION:Title: Cosmetic Surgeries on Knots and Heegaard Floer Homology \nAbstract: A common method of constructing 3-manifolds is via Dehn surgery on knots. A pair of surgeries on a knot is called purely cosmetic if the resulting 3-manifolds are homeomorphic as oriented manifolds\, whereas it is said to be chirally cosmetic if they result in homeomorphic manifolds with opposite orientations. An outstanding conjecture predicts that no nontrivial knots admit any purely cosmetic surgeries. We apply certain obstructions from Heegaard Floer homology to show that (nontrivial) knots which arise as the closure of a 3-stranded braid do not admit any purely cosmetic surgeries. Furthermore\, we find new obstructions to the existence of chirally cosmetic surgeries coming from Heegaard Floer homology; in particular\, we make use of immersed curve formulations of knot Floer homology and the corresponding surgery formula. Combining these with other obstructions involving finite type invariants\, we completely classify chirally cosmetic surgeries on odd alternating pretzel knots. Moreover\, we rule out cosmetic surgeries for L-space knots along slopes with opposite signs.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-konstantinos-varvarezos-ucla/
LOCATION:Fletcher 110\, Pitzer College\, 1050 N Mills Ave\, Claremont\, CA\, 91711\, United States
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231101T161500
DTEND;TZID=America/Los_Angeles:20231101T173000
DTSTAMP:20260425T074359
CREATED:20231030T223857Z
LAST-MODIFIED:20231030T223857Z
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SUMMARY:Slope Gap Distributions of Translation Surfaces (Taylor McAdam\, Pomona College)
DESCRIPTION:Title: Slope gap distributions of translation surfaces \nSpeaker: Taylor McAdam\, Department of Mathematics\, Pomona College \nAbstract: How “random” are the rational numbers? To make sense of this question\, let us consider the set of Farey fractions of level n—that is\, the rational numbers between 0 and 1 with denominator at most n. It turns out that these distribute uniformly in the unit interval as n goes to infinity\, which would suggest they appear to be quite random. However\, we may consider a finer test of randomness by considering the distribution of gaps between consecutive Farey fractions as n tends to infinity. To investigate this\, we will first realize the Farey fractions as the slopes of geodesic paths on the (square) flat torus—a geometric object obtained by gluing the opposite edges of a square together. We will then define the horocycle flow on the space of all flat tori\, which will allow us to study our question about gaps between Farey fractions via a dynamical system. Finally\, we will see how this method can be generalized to study the slope gap distributions for paths on a larger class of geometric objects called translation surfaces and discuss results on the collection of surfaces obtained by gluing together opposite edges of the regular 2n-gon.\n\n\n\n\n\n\nTaylor McAdam graduated with a Bachelor’s degree in mathematics from Harvey Mudd College in 2013 before starting a doctoral program at University of Texas at Austin. In 2017\, she transferred to the University of California San Diego\, where she received her PhD in mathematics in 2019 under the supervision of Amir Mohammadi. She was an NSF Postdoctoral Fellow at Yale University from 2019 to 2023\, before joining the faculty at Pomona College in 2023 as a Visiting Assistant Professor. Her research interests lie at the intersection of dynamical systems\, geometry\, and number theory\, and she is passionate about undergraduate math education and building inclusive mathematical communities.
URL:https://colleges.claremont.edu/ccms/event/slope-gap-distributions-of-translation-surfaces-taylor-mcadam-pomona-college/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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DTSTART;TZID=America/Los_Angeles:20231104T100000
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SUMMARY:GEMS November 4th Session
DESCRIPTION:
URL:https://colleges.claremont.edu/ccms/event/gems-november-4th-session/
LOCATION:Shanahan 1480\, Harvey Mudd College\, 301 Platt Blvd.\, Claremont\, CA\, 91711\, United States
CATEGORIES:GEMS
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