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DTSTART;TZID=America/Los_Angeles:20230321T121500
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DTSTAMP:20260415T163921
CREATED:20230113T153459Z
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UID:3025-1679400900-1679404200@colleges.claremont.edu
SUMMARY:Robust properties of graphs (Asaf Ferber\, UC Irvine)
DESCRIPTION:In this talk we will consider some notions of `robustness’ of graph/hypergraph properties. We will survey some existing results and will try to emphasize the following new result (joint with Adva Mond and Kaarel Haenni): The binomial random digraph $D_{n\,p}$ typically contains the minimum between the minimum out- and in-degrees many edge-disjoint Hamilton cycles\, given that $p\geq \log^C n/n$. The result is optimal up to log factors.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-asaf-ferber-uc-irvine/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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CREATED:20230124T212708Z
LAST-MODIFIED:20230320T225330Z
UID:3054-1680005700-1680009000@colleges.claremont.edu
SUMMARY:The Smith normal form of a polynomial of a random integral matrix (Gilyoung Cheong\, UC Irvine)
DESCRIPTION:Given a prime p\, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0\,1)-matrix over the same ring. We compute the asymptotic distribution of the cokernel of P(X(n)) as n goes to infinity. When P(t) is square-free modulo p\, this lets us compute the asymptotic distribution of the Smith normal form of P(X(n)). In fact\, we shall consider the same problem with a more general random matrix X(n)\, which also includes the example of a Haar-random matrix. Our work crucially uses a recent work of W. Sawin and M. M. Wood which shows that the moments of finite size modules over any ring determine their distribution.\n\nThis is joint work with Myungjun Yu. https://arxiv.org/abs/2303.09125
URL:https://colleges.claremont.edu/ccms/event/antc-talk-gilyoung-cheong-uci/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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