| Jinyoung Park from Institute for Advanced Study, Princeton | Jinyoung Park from Institute for Advanced Study, Princeton | Zoom | <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 PM | 12/4/2020 7:20:00 PM | False | |
| Lisa Sauermann, Institute for Advanced Study, Princeton | Lisa Sauermann, Institute for Advanced Study, Princeton | Zoom | <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 PM | 11/20/2020 7:20:00 PM | False | |
| Joshua Cooper, University of South Carolina | Joshua Cooper, University of South Carolina | Zoom | Title: Around the Brouwer Conjecture <br>
Abstract: <a href="https://www.mathsci.udel.edu/content-sub-site/Documents/absDM.pdf">Abstract</a> | 11/5/2020 6:00:00 PM | 11/5/2020 7:00:00 PM | False | |
| Melissa Fuentes, University of Delaware | Melissa Fuentes, University of Delaware | Zoom | <br>Title: Maximum Number of q-Colorings of Graphs with a Fixed Number of Vertices
and Edges <br>
<br><a>https://www.mathsci.udel.edu/content-sub-site/Documents/MF_Abstract.pdf</a><br> | 10/30/2020 8:00:00 PM | 10/30/2020 9:00:00 PM | False | |
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