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DTSTART;TZID=America/Los_Angeles:20231009T161500
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DTSTAMP:20260511T065622
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SUMMARY:Applied Math Seminar: Dan Pirjol (Stevens Institute of Technology)
DESCRIPTION:Title: The Hartman-Watson distribution: numerical evaluation and applications in mathematical finance \nAbstract: The Hartman-Watson distribution appears in several problems of applied probability and financial mathematics. Most notably\, it determines the joint distribution of the time-integral of a geometric Brownian motion and its terminal value. A classical result by Yor (1981) expresses it as a one-dimensional integral which is however difficult to evaluate numerically in the region of interest for financial applications. The talk gives an introduction to the HW distribution and presents an asymptotic expansion which can be used for an efficient numerical evaluation. Two applications from mathematical finance are discussed: Asian options pricing in the Black-Scholes model\, and option pricing in the log-normal SABR model.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-dan-pirjol-stevens-institute-of-technology/
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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DTSTART;TZID=America/Los_Angeles:20231010T150000
DTEND;TZID=America/Los_Angeles:20231010T160000
DTSTAMP:20260511T065622
CREATED:20230915T192038Z
LAST-MODIFIED:20231006T052904Z
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SUMMARY:Claremont Topology Seminar: Christopher Perez (Loyola University New Orleans)
DESCRIPTION:Title: Towers and elementary embeddings in total relatively hyperbolic groups \nAbstract: In a remarkable series of papers\, Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers. It was later proved by Chloé Perin that if H is an elementarily embedded subgroup (or elementary submodel) of a torsion-free hyperbolic group G\, then G is a tower over H. We prove a generalization of Perin’s result to toral relatively hyperbolic groups using JSJ and shortening techniques.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-christopher-perez-loyola-university-new-orleans/
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
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DTSTART;TZID=America/Los_Angeles:20231011T161500
DTEND;TZID=America/Los_Angeles:20231011T173000
DTSTAMP:20260511T065622
CREATED:20231003T221601Z
LAST-MODIFIED:20231003T221601Z
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SUMMARY:Equality Cases of Geometric Inequalities (Igor Pak\, UCLA)
DESCRIPTION:Title: Equality Cases of Geometric Inequalities \nSpeaker: Igor Pak\, Department of Mathematics\, University of California\, Los Angeles \nAbstract: Geometric inequalities go back to antiquity\, and so do their equality cases.  As everyone knows\, the circle is the only case when the isoperimetric inequality is sharp.  But what happens to other geometric inequalities?  Apparently\, as the inequalities become more general\, their equality cases become more cumbersome to state and even harder to prove.  I will give a broad survey of various natural examples\, with an emphasis on discrete inequalities.  I will then explain why the celebrated Alexandrov–Fenchel inequality has intractable equality cases\, what does that mean\, and how this can be established.  The talk is aimed at a general audience.
URL:https://colleges.claremont.edu/ccms/event/equality-cases-of-geometric-inequalities-igor-pak-ucla/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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