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DTSTART;TZID=America/Los_Angeles:20240226T161500
DTEND;TZID=America/Los_Angeles:20240226T171500
DTSTAMP:20260406T004621
CREATED:20240220T215244Z
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SUMMARY:Javier Gonzalez Anaya (Harvey Mudd College)
DESCRIPTION:This is the continuation of the semester’s joint seminar with the Universidad Nacional de Colombia-Manizales. \nTitle: Enumerating linearity regions of max-pooling layers in convolutional neural networks \nAbstract: Convolutional neural networks (CNN’s) are central tools in the application of machine learning to text\, audio and image processing. Their success stems from the ability of these networks to identify key features in complex datasets at a relatively low computational cost. Max-pooling layers (MPL’s) are key components of CNN’s that reduce the number of parameters used by the network while making it more robust to small changes in the input data. From a mathematical point of view\, MPLs are piecewise-linear functions\, and their number of linearity regions can be interpreted as a measure of complexity of the layer. In this talk I will explain how we can use combinatorial techniques to count these linearity regions\, and survey our current results in the area.
URL:https://colleges.claremont.edu/ccms/event/javier-gonzalez-anaya-harvey-mudd-college/
LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, 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:20240227T121500
DTEND;TZID=America/Los_Angeles:20240227T131000
DTSTAMP:20260406T004621
CREATED:20240126T230120Z
LAST-MODIFIED:20240221T014138Z
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SUMMARY:The restricted variable Kakeya problem (Pete Clark\, University of Georgia)
DESCRIPTION:For a finite field F_q\, a subset of F_q^N is a Kakeya set if it contains a line in every direction (i.e.\, a coset of every one-dimensional linear subspace).  The finite field Kakeya problem is to determine the minimal size K(N\,q) of a Kakeya set in F_q^N.  This problem was posed by Wolff in 1999 as an analogue to the Kakeya problem in Euclidean N-space\, which was (and still is) one of the major open problems in harmonic analysis.  It caused quite a stir in 2008 when Zeev Dvir showed that for each fixed N\, as q -> oo\, K(N\,q) is bounded below by a constant times q^N: the Euclidean analogue of this result is not only proved but known to be false.\n\nBut what about the constant?  In 2009 Dvir-Kopparty-Saraf-Sudan gave a lower bound on K(N\,q) that was within a factor of 2 of an upper bound due to Dvir-Thas.  (I will briefly mention recent work of Bukh-Chao giving a decisive further improvement\, but that is not the focus of the talk.) The key to this improved lower bound is a multiplicity enhancement of a 1922 result of Ore. In this talk I want to give my own exposition of this work together with a mild generalization: if X is a subset of F_q^N \ {0}\, then an X-Kakeya set is a subset that contains a translate of the line generated by x for all x in X.  Putting K_X(N\,q) to be the minimal size of an X-Kakeya set in F_q^N\, I will give a lower bound on K_X(N\,q) that recovers the DKSS bound when X = F_q^N \ {0}.  This is similar in spirit to  “statistical Kakeya” results of Dvir and DKSS but not overlapping much; in fact\, I will give a statistical generalization of my result as well.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-pete-clark-university-of-georgia/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20240227T150000
DTEND;TZID=America/Los_Angeles:20240227T160000
DTSTAMP:20260406T004621
CREATED:20240128T225822Z
LAST-MODIFIED:20240224T002645Z
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SUMMARY:Claremont Topology Seminar: No Seminar
DESCRIPTION:No Seminar
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-orsola-capovilla-searle-uc-davis/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
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DTSTART;TZID=America/Los_Angeles:20240228T161500
DTEND;TZID=America/Los_Angeles:20240228T173000
DTSTAMP:20260406T004621
CREATED:20240222T005317Z
LAST-MODIFIED:20240222T005317Z
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SUMMARY:A Group-Theoretic Ax-Katz Theorem (Pete L. Clark\, University of Georgia)
DESCRIPTION:Title: A Group-Theoretic Ax-Katz Theorem \nSpeaker: Pete L. Clark\, University of Georgia \nAbstract: The Chevalley-Warning Theorem is a result from 1935 asserting that the number of solutions to a low degree polynomial system over a finite field is divisible by the characteristic of the field.  It is an important result — it includes a conjecture of Artin and Dickson from the 1920’s — but it is not difficult to prove: the original proof is about three pages.  In 1964 James Ax gave a completely elementary ten line proof.   In the same paper\, Ax showed that as the number and degrees of the polynomials are held fixed and the number of variables increases\, not only is the size of the solution set divisible by p but by higher and higher powers of p.  The best possible p-adic divisibility here was given in 1971 by Nicholas Katz.  Katz’s proof is at a much higher level: you need specialist knowledge in the right subfields of number theory to understand it.  Simpler proofs were found later\, but none fulfills the fantasy of generalizing Ax’s ten line proof of Chevalley-Warning. \nA 2021 work of Aichinger-Moosbauer develops a fully fledged calculus of finite differences for maps between commutative groups and uses it to give a purely group-theoretic generalization of Chevalley-Warning. Nicholas Triantafillou and I have used and extended this work: up to a few black boxes (where most of the content is indeed hidden) we give a ten line proof of a group-theoretic analogue of Ax-Katz that “qualitatively fulfills my fantasy.”\n\n\n\n\n\nIn (North)west Philadelphia was Pete L. Clark born and raised.  He received undergraduate and masters degrees from the University of Chicago and a PhD from Harvard University.  He has worked in the Mathematics Department at the University of Georgia since 2006\, where he was the Graduate Coordinator from 2016-2019 and where he is now the Principal Honors Advisor.  When time permits he is an avid reader\, and his favorite authors include Ralph Ellison\, Jonathan Franzen\, Kazuo Ishiguro\, Carmen Maria Machado and Lorrie Moore.
URL:https://colleges.claremont.edu/ccms/event/a-group-theoretic-ax-katz-theorem-pete-l-clark-university-of-georgia/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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SUMMARY:GEMS March 2nd Session
DESCRIPTION:
URL:https://colleges.claremont.edu/ccms/event/gems-march-2nd-session/
LOCATION:Harvey Mudd College at the Shanahan Teaching and Learning Center\, 301 Platt Blvd.\, Claremont\, CA\, 91711\, United States
CATEGORIES:GEMS
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