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DTSTART;TZID=America/Los_Angeles:20181002T121500
DTEND;TZID=America/Los_Angeles:20181002T131000
DTSTAMP:20260516T102543
CREATED:20180911T213738Z
LAST-MODIFIED:20180926T151643Z
UID:533-1538482500-1538485800@colleges.claremont.edu
SUMMARY:An Introduction to the Sato-Tate Conjecture (Edray Goins\, Pomona College)
DESCRIPTION:In 1846\, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.  This was forgotten about for nearly 100 years until John von Neumann and Herman Goldstine attempted to verify the conjecture as a way to test the new ENIAC machine in 1953.  They found evidence that the conjecture was false\, but trusted Kummer more than they did their digital computer.  The conjecture would hold until 1979\, when Roger Heath-Brown and Samuel Patterson proved it to be false. \nA few years earlier in 1965\, Mikio Sato and John Tate independently came up with a conjecture which gave the correct distribution of these cubic Gauss sums — although it was expressed slightly differently in terms of counting points of elliptic curves over finite fields.  In this talk\, we give an overview of the Sato-Tate Conjecture\, present an approach by Jean-Pierre Serre following his paper from 1967\, then sketch the 2006 proof of the conjecture following the ideas of Laurent Clozel\, Michael Harris\, Nicholas Shepherd-Barron and Richard Taylor. \nHere are the slides of this lecture: Edray Goins’ slides.
URL:https://colleges.claremont.edu/ccms/event/talk-by-edray-goins-pomona-college/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181009T121500
DTEND;TZID=America/Los_Angeles:20181009T131000
DTSTAMP:20260516T102543
CREATED:20180912T160739Z
LAST-MODIFIED:20181001T220127Z
UID:546-1539087300-1539090600@colleges.claremont.edu
SUMMARY:State Polytopes of Combinatorial Neural Codes (Rob Davis\, HMC)
DESCRIPTION:Combinatorial neural codes are 0/1 vectors that are used to model the co-firing patterns of a set of place cells in the brain. One wide-open problem in this area is to determine when a given code can be algorithmically drawn in the plane as a Venn diagram-like figure. A sufficient condition to do so is for the code to have a property called k-inductively pierced. Gross\, Obatake\, and Youngs recently used toric algebra to show that a code on three neurons is 1-inductively pierced if and only if the toric ideal is trivial or generated by quadratics. No result is known for additional neurons in the same generality. \nIn this talk\, we study two infinite classes of combinatorial neural codes in detail. For each code\, we explicitly compute its universal Gröbner basis. This is done for the first class by recognizing that the codewords form a Lawrence-type matrix. With the second class\, this is done by showing that the matrix is totally unimodular. These computations allow one to compute the state polytopes of the corresponding toric ideals\, from which all distinct initial ideals may be computed efficiently. Moreover\, we show that the state polytopes are combinatorially equivalent to well-known polytopes: the permutohedron and the stellohedron.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-rob-davis-hmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181016T121500
DTEND;TZID=America/Los_Angeles:20181016T131000
DTSTAMP:20260516T102543
CREATED:20181008T194923Z
LAST-MODIFIED:20181008T194923Z
UID:897-1539692100-1539695400@colleges.claremont.edu
SUMMARY:The Bateman—Horn Conjecture\, Part I: heuristic derivation (Stephan Garcia\, Pomona)
DESCRIPTION:The Bateman—Horn Conjecture is a far-reaching statement about the distribution of the prime numbers.  It implies many known results\, such as the Green—Tao theorem\, and a variety of famous conjectures\, such as the Twin Prime Conjecture.  In this expository talk\, we start from basic principles and provide a heuristic argument in favor of the conjecture.  This talk should be accessible to undergraduates with a background in modular arithmetic.
URL:https://colleges.claremont.edu/ccms/event/the-bateman-horn-conjecture-part-i-heuristic-derivation-stephan-garcia-pomona/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181030T121500
DTEND;TZID=America/Los_Angeles:20181030T131000
DTSTAMP:20260516T102543
CREATED:20180823T224159Z
LAST-MODIFIED:20181024T083012Z
UID:471-1540901700-1540905000@colleges.claremont.edu
SUMMARY:Uniform asymptotic growth of symbolic powers  (Robert Walker\, University of Michigan)
DESCRIPTION:Algebraic geometry (AG) is a major generalization of linear algebra which is fairly influential in mathematics. Since the 1980’s with the development of computer algebra systems like Mathematica\, AG has been leveraged in areas of STEM as diverse as statistics\, robotic kinematics\, computer science/geometric modeling\, and mirror symmetry. Part one of my talk will be a brief introduction to AG\, to two notions of taking powers of ideals (regular vs symbolic) in Noetherian commutative rings\, and to the ideal containment problem that I study in my thesis. Part two of my talk will focus on stating the main results of my thesis in a user-ready form\, giving a “comical” example or two of how to use them. At the risk of sounding like Paul Rudd in Ant-Man\, I hope this talk with be awesome.
URL:https://colleges.claremont.edu/ccms/event/tba-4/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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