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DTSTART;TZID=America/Los_Angeles:20200204T121500
DTEND;TZID=America/Los_Angeles:20200204T131000
DTSTAMP:20260407T183037
CREATED:20200129T003031Z
LAST-MODIFIED:20200129T003031Z
UID:1831-1580818500-1580821800@colleges.claremont.edu
SUMMARY:Covering point-sets with parallel hyperplanes and sparse signal recovery (Lenny Fukshansky\, CMC)
DESCRIPTION:Let S be a set of k > n points in n-dimensional Euclidean space. How many parallel hyperplanes are needed to cover it? In fact\, it is easy to prove that every such set can be covered by k-n+1 parallel hyperplanes\, but do there exist sets that cannot be covered by fewer parallel hyperplanes? We construct a family of examples of such extremal sets. We then use it\, along with a result on girth of bipartite graphs\, to construct a family of n x d integer matrices with bounded sup-norm and the property that no m column vectors are linearly dependent\, m < n. If m < (log n)^{1-e} for any e > 0\, then d/n tends to infinity as n tends to infinity. This is a deterministic construction of a family of sensing matrices\, which are used for sparse signal recovery in compressed sensing. Joint work with Alex Hsu.
URL:https://colleges.claremont.edu/ccms/event/covering-point-sets-with-parallel-hyperplanes-and-sparse-signal-recovery-lenny-fukshansky-cmc/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20200211T121500
DTEND;TZID=America/Los_Angeles:20200211T131000
DTSTAMP:20260407T183037
CREATED:20200129T000815Z
LAST-MODIFIED:20200202T234446Z
UID:1823-1581423300-1581426600@colleges.claremont.edu
SUMMARY:Quandle module quivers (Sam Nelson\, CMC)
DESCRIPTION:Quandle coloring quivers categorify the quandle counting invariant. In this talk we enhance the quandle coloring quiver invariant with quandle modules\, generalizing both the quiver invariant and the quandle module polynomial invariant. This is joint work with Karma Istanbouli (Scripps College).
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-sam-nelson-cmc/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20200218T121500
DTEND;TZID=America/Los_Angeles:20200218T131000
DTSTAMP:20260407T183037
CREATED:20191221T204555Z
LAST-MODIFIED:20200201T061024Z
UID:1699-1582028100-1582031400@colleges.claremont.edu
SUMMARY:On badly approximable numbers (Nikolai Moshchevitin\, Moscow State University)
DESCRIPTION:It is well known that a real number is badly approximable if and only if the partial quotients in its continued fraction expansion are bounded. Motivated by a recent wonderful paper by Ngoc Ai Van Nguyen\, Anthony Poels and Damien Roy (where the authors give a simple alternative solution of Schmidt-Summerer’s problem) we found an unusual generalization of this criterion for badly approximable d-dimensional vectors.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-nikolai-moshchevitin-moscow-state-university/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20200225T121500
DTEND;TZID=America/Los_Angeles:20200225T131000
DTSTAMP:20260407T183037
CREATED:20190809T161558Z
LAST-MODIFIED:20200202T224846Z
UID:1355-1582632900-1582636200@colleges.claremont.edu
SUMMARY:Discrepancy theory and related questions (Dmitriy Bilyk\, University of Minnesota)
DESCRIPTION:The talk will concentrate on open questions related to the optimal bounds for the discrepancy of an $N$-point set in the $d$-dimensional unit cube. The so-called star-discrepancy measures the difference between the actual and expected number of points in axis-parallel rectangles\, and thus measures the equidistribution of the set. This notion has been explored by H. Weyl\, K. Roth\, and many others\, however many questions still remain open\, especially in higher dimensions.  We shall discuss the two main conjectures on the order of star-discrepancy and present evidence in support of each one\, as well as their connections to various areas of mathematics. In addition\, we shall talk about discrepancy in other geometrical settings (rotated rectangles\, balls\, points on the sphere etc).
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-dmitriy-bilyk-university-of-minnesota/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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