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DTSTART;TZID=America/Los_Angeles:20250407T161500
DTEND;TZID=America/Los_Angeles:20250407T171500
DTSTAMP:20260408T221421
CREATED:20250402T004832Z
LAST-MODIFIED:20250402T004832Z
UID:3749-1744042500-1744046100@colleges.claremont.edu
SUMMARY:Applied Math Seminar: Ethan Epperly (Caltech)
DESCRIPTION:Title: Randomly pivoted Cholesky: Fast\, accurate matrix approximation for scientific machine learning \nAbstract:\nLow-rank approximation of positive semidefinite matrices is a basic problem in computational mathematics\, with many applications to machine learning and scientific computing. Existing approaches for this problem largely fall into two categories: simple\, fast\, but sometimes inaccurate methods and sophisticated\, slower methods with accuracy guarantees. To achieve the best of both worlds\, this talk introduces randomly pivoted Cholesky\, an algorithm for positive semidefinite low-rank approximation that is simple\, fast\, and accurate. We demonstrate the effectiveness of randomly pivoted Cholesky for spectral clustering of molecular dynamics data\, achieving an order of magnitude lower clustering error than previous methods. We then go on to discuss theoretical guarantees for randomly pivoted Cholesky. Using a matrix concavity argument\, we show that randomly pivoted Cholesky has nearly optimal low-rank approximation properties. We conclude by discussing extensions and future prospects for this simple\, yet effective\, algorithm.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-ethan-epperly-caltech/
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:20250408T121500
DTEND;TZID=America/Los_Angeles:20250408T131000
DTSTAMP:20260408T221421
CREATED:20250212T050525Z
LAST-MODIFIED:20250407T150550Z
UID:3692-1744114500-1744117800@colleges.claremont.edu
SUMMARY:The ANTC of ChatGPT: On the Mathematical Foundations of Large Language Models (Gizem Karaali\, Pomona)
DESCRIPTION:Large Language Models like ChatGPT rely on surprisingly familiar mathematics. This talk will explore how ideas from (linear) algebra\, number theory and combinatorics  appear — both directly and indirectly — in the structure and behavior of these models. Along the way\, we’ll touch on themes like structure\, symmetry\, and scale\, and consider how abstract mathematical ideas can shed light on systems that process and generate human language. The talk will be self-contained\, and no background in machine learning will be assumed. (This abstract was prepared with the assistance of ChatGPT\, which seems to be remarkably self-aware of its own mathematical foundations.)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-gizem-karaali-pomona-3/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20250409T161500
DTEND;TZID=America/Los_Angeles:20250409T173000
DTSTAMP:20260408T221421
CREATED:20250131T234941Z
LAST-MODIFIED:20250409T232205Z
UID:3676-1744215300-1744219800@colleges.claremont.edu
SUMMARY:CCMS Colloquium presents "Fall 2025 Course Preview Session"
DESCRIPTION:Fall 2025 Course Preview Session \nModerator: Lenny Fukshansky\, Professor of Mathematics\, Claremont McKenna College\, CA \nSlide Link: https://docs.google.com/presentation/d/142NF1vUazpGNLF0pfLKc0qhkv4VoMQstSvZ0yKtMfNE/edit?usp=sharing
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-presents-fall-2025-course-preview-session/
LOCATION:CA
CATEGORIES:Colloquium
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