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DTSTART;TZID=America/Los_Angeles:20250908T161500
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DTSTAMP:20260614T204541
CREATED:20250829T233038Z
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SUMMARY:The Shooting Method in the Analysis of Two-Point Boundary-Value Problems (Adolfo J. Rumbos\, Pomona College)
DESCRIPTION:Abstract: \nTwo-point boundary-value problems (BVPs) appear frequently in applied mathematics.  When looking for solutions of boundary-value problems for some partial differential equations (PDEs) in mathematical physics\, two-point BVPs come up as a result of applying the method of separation of variables\, for instance. In the case of linear PDEs\, the resulting two-point BVPs fall into a class of problems known as Sturm-Liouville eigenvalue problems. \nThis presentation deals with the use of the shooting method to prove existence of solutions of two-point BVPs.  The shooting method is a numerical technique used to estimate solutions of two-point BVPs once a solution is known to exist.  In this talk we illustrate how the shooting method can be used to prove existence of eigenvalues of linear Sturm-Liouville problems.  We also show how the shooting method can be applied to prove existence and uniqueness of solutions for some nonlinear\, two-point BVPs\, and existence of eigenvalues for some nonlinear eigenvalue problems. \nThe presentation describes research conducted with collaborators Vaidehi Srinivasan (Pomona College class of 2027) and Gavin Zhao (Pomona College class of 2029) in the summer of 2025 with the support of the Summer Undergraduate Research Program at Pomona College.
URL:https://colleges.claremont.edu/ccms/event/the-shooting-method-in-the-analysis-of-two-point-boundary-value-problems-adolfo-j-rumbos-pomona-college/
LOCATION:CA
CATEGORIES:Applied Math Seminar
ORGANIZER;CN="Ryan Aschoff":MAILTO:ryan.aschoff@cgu.edu
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DTSTART;TZID=America/Los_Angeles:20250912T110000
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LAST-MODIFIED:20250909T001255Z
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SUMMARY:CCMS Colloquium: Morse theory\, Floer homology\, and string topology (Ko Honda\, UCLA)
DESCRIPTION:CCMS Colloquium invites you to a talk by Professor Ko Honda\, Professor of Mathematics at UCLA. \nTitle: Morse theory\, Floer homology\, and string topology \nAbstract: One of the most important theories in geometry/topology is Floer homology\, which can be viewed as a Morse theory of a loop space of a manifold (a generalization of a surface to higher dimensions).  The aim of this talk is to give a gentle pictorial introduction to Morse theory for surfaces and then upgrade it in two steps: to Morse theory of loop spaces (e.g.\, of the 2-dimensional sphere) and then to “multiloops” (collections of many loops).  The last upgrade is intimately related to a mathematical model for string theory called “string topology”\, due to Chas-Sullivan\, and to quantum topology via the HOMFLY polynomial of knots/links. \nSpeaker Bio: Ko Honda is an entirely American-trained mathematician\, receiving his BA and MA from Harvard University in 1992 and PhD from Princeton University in 1997.  After postdocs/visiting positions at Duke\, the University of Georgia\, the American Institute of Mathematics\, and IHES\, he arrived in LA in 2001\, was a faculty member at USC for 12.5 years\, and then moved across town to UCLA\, where he has been for the last 11.5 years.  Sometime during his postdoc at Duke\, he discovered/invented an object called a “bypass” in contact geometry\, which allowed him to simplify the analysis of 3-dimensional contact manifolds and solve several open problems in that area\, some in joint work with Colin\, Etnyre\, and Giroux.  He has been working on contact and symplectic geometry ever since\, gradually branching out into adjacent areas (e.g.\, low-dimensional topology\, Floer theory\, and quantum topology) in the intervening years.
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-presents-title-ko-honda/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
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