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Archive : Discrete Mathematics

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Jinyoung Park from Institute for Advanced Study, PrincetonJinyoung Park from Institute for Advanced Study, PrincetonZoom<br> Title: The threshold for the square of a Hamilton cycle<br> Abstract: I will first introduce some basics about random graph theory, mostly focusing on thresholds for increasing properties, such as Hamiltonicity or subgraph containment. After that, we will talk about a recent result of Jeff Kahn, Bhargav Narayanan, and myself stating that the threshold for the random graph G(n,p) to contain the square of a Hamilton cycle is 1/sqrt n, resolving a conjecture of Kühn and Osthus from 2012. The proof idea is motivated by the recent work of Frankston and the three aforementioned authors on a conjecture of Talagrand -- "a fractional version of Kahn-Kalai expectation threshold conjecture."12/4/2020 6:20:00 PM12/4/2020 7:20:00 PMFalse
Lisa Sauermann, Institute for Advanced Study, PrincetonLisa Sauermann, Institute for Advanced Study, PrincetonZoom<br>Title: On polynomials that vanish to high order on most of the hypercube <br> <br>Abstract: Motivated by higher vanishing multiplicity generalizations of Alon's Combinatorial Nullstellensatz and its applications, we study the following problem: for fixed k and n large with respect to k, what is the minimum possible degree of a polynomial P in R[x_1,...,x_n] such that P(0,…,0) is non-zero and such that P has zeroes of multiplicity at least k at all points in {0,1}^n except the origin? For k=1, a classical theorem of Alon and Füredi states that the minimum possible degree of such a polynomial equals n. We solve the problem for all k>1, proving that the answer is n+2k−3. Joint work with Yuval Wigderson. <br> 11/20/2020 6:20:00 PM11/20/2020 7:20:00 PMFalse
Joshua Cooper, University of South CarolinaJoshua Cooper, University of South CarolinaZoomTitle: Around the Brouwer Conjecture <br> Abstract: <a href="">Abstract</a>11/5/2020 6:00:00 PM11/5/2020 7:00:00 PMFalse
Melissa Fuentes, University of DelawareMelissa Fuentes, University of DelawareZoom<br>Title: Maximum Number of q-Colorings of Graphs with a Fixed Number of Vertices and Edges <br> <br><a></a><br>10/30/2020 8:00:00 PM10/30/2020 9:00:00 PMFalse

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