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DTSTART;TZID=America/Los_Angeles:20250324T161500
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SUMMARY:Applied Math Seminar: Ryan O'Dowd (Claremont Graduate University)
DESCRIPTION:Title: Learning on manifolds without manifold learning \nAbstract: Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional Euclidean space. A great deal of research deals with obtaining information about this manifold\, such as the eigendecomposition of the Laplace-Beltrami operator or coordinate charts\, and using this information for function approximation. This two-step approach implies some extra errors in the approximation stemming from estimating the basic quantities of the data manifold in addition to the errors inherent in function approximation. In this paper\, we project the unknown manifold as a submanifold of an ambient hypersphere and study the question of constructing a one-shot approximation using a specially designed sequence of localized spherical polynomial kernels on the hypersphere. Our approach does not require preprocessing of the data to obtain information about the manifold other than its dimension. We give optimal rates of approximation for relatively “rough” functions.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-ryan-odowd-claremont-graduate-university/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Applied Math Seminar
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DTSTART;TZID=America/Los_Angeles:20250325T121500
DTEND;TZID=America/Los_Angeles:20250325T131000
DTSTAMP:20260620T084241
CREATED:20250127T201036Z
LAST-MODIFIED:20250324T151237Z
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SUMMARY:Some Diophantine analogies between Dirichlet series and polynomials (Vesselin Dimitrov\, Caltech)
DESCRIPTION:I will present an integral — requiring no character twists — converse theorem for recognizing when is a Dirichlet series with algebraic integer coefficients equal to the L-function of a modular form. This refines the unbounded denominators conjecture of Atkin and Swinnerton-Dyer. Analogies with basic function field arithmetic then suggest a quantitative refinement which precludes a pair of GL(2) automorphic L-functions with closely matched up zeros. I will explain how to get at such a theorem. 
URL:https://colleges.claremont.edu/ccms/event/antc-talk-vesselin-dimitrov-caltech/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20250325T150000
DTEND;TZID=America/Los_Angeles:20250325T160000
DTSTAMP:20260620T084241
CREATED:20250214T211453Z
LAST-MODIFIED:20250324T000533Z
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SUMMARY:Claremont Topology Seminar: Reginald Anderson (Claremont McKenna College)
DESCRIPTION:We especially welcome all undergraduates and graduate students to attend topology seminar! \nSpeaker: Reginald Anderson (Claremont McKenna College) \nTitle: Kontsevich’s Recursive Formula for Rational Plane Curves \nAbstract: Gromov-Witten theory was developed in the 1990s as a curve-counting theory by integrating cohomology classes against a virtual fundamental class for a moduli space of stable maps. One early success of the theory was Kontsevich’s recursive formula for enumerating the number of rational plane curves through 3d-1 points in general position. Starting from a consideration of which genus 0 Gromov-Witten invariants for the complex projective plane can possibly be non-zero\, we will assemble a generating function for these invariants\, called the genus 0 Gromov-Witten potential for the complex projective plane. If time allows\, we will also use the fact that the potential satisfies a partial differential equation called the Witten-Dijkgraaf-Verlinde-Verlinde equation to solve for N_d\, the coefficients of the generating function\, which give the number of rational plane curves through 3d-1 points. \nThis talk follows p. 24-26 of these notes\, available at https://arxiv.org/abs/2501.03232. \nAll are welcome.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-reginald-anderson-claremont-mckenna-college/
LOCATION:Estella 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, United States
CATEGORIES:Topology Seminar
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DTSTART;TZID=America/Los_Angeles:20250326T161500
DTEND;TZID=America/Los_Angeles:20250326T173000
DTSTAMP:20260620T084241
CREATED:20250201T220938Z
LAST-MODIFIED:20250326T201510Z
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SUMMARY:CCMS Colloquium: Brownian Motion\, Random Fractals\, and Beyond (Yimin Xiao\, Michigan State Uni)
DESCRIPTION:Speaker: Yimin Xiao\, Professor of Statistics and Probability\, Michigan State University \nTitle: Brownian Motion\, Random Fractals\, and Beyond \nAbstract: Brownian motion is not only a fascinating object in mathematics but also a powerful stochastic model that has been applied in many scientific fields\, from physics to finance\, to biological sciences. The sample function of Brownian motion is nowhere differentiable and generates various interesting fractal sets and measures. It is natural to apply tools from Fractal Geometry (e.g. Hausdorf dimension\, packing dimension) to study the fine properties of Brownian motion. There is an enormous literature on sample path properties of Brownian motion\, including many fractal and multifractal properties.\nIn this talk\, we first provide an overview of some regularity and fractal properties of Brownian motion and its local times. These results are fundamental for the development of related theories for other stochastic processes. We then describe extensions of these results to Levy stable processes and fractional Brownian motion\, which are two important relatives of Brownian motion in the areas of Markov processes and Gaussian processes\, respectively. \nBio: Yimin Xiao is an MSU Research Foundation Professor in Statistics and Probability at Michigan State University. He received his Ph.D. from the Ohio State University in 1996. After completing his postdocs at the University of Utah and Microsoft Research\, he joined Michigan State University in 2000. His research interests include random fields\, Gaussian and Lévy processes\, stochastic partial differential equations\, extreme value theory\, random fractals\, and statistical analysis of spatial and spatio-temporal models. He has published about 160 articles in peer-reviewed journals. \nDr. Xiao has been a visiting professor at several universities in China\, France\, Germany\, Hong Kong\, Sweden\, and Switzerland and has been invited as a speaker at various international conferences. He is a Fellow of the Institute of Mathematical Statistics. \n 
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-brownian-motion-random-fractals-and-beyond-yimin-xiao-michigan-state-uni/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
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