Ting-Wei Chao (趙庭偉), Tight Bound on Joints Problem and Partial Shadow Problem
Given a set of lines in $\mathbb R^d$, a joint is a point contained in d linearly independent lines. Guth and Katz showed that N lines can determine at most …
10 events found.
Discrete Math Seminar
Events
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Room B332 IBS (기초과학연구원)
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Shengtong Zhang (张盛桐), Triangle Ramsey numbers of complete graphs
Room B332 IBS (기초과학연구원)A graph is $H$-Ramsey if every two-coloring of its edges contains a monochromatic copy of $H$. Define the $F$-Ramsey number of $H$, denoted by $r_F(H)$, to be the minimum number …
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Daniel McGinnis, Applications of the KKM theorem to problems in discrete geometry
Room B332 IBS (기초과학연구원)We present the KKM theorem and a recent proof method utilizing it that has proven to be very useful for problems in discrete geometry. For example, the method was used …
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Jinyoung Park (박진영), Dedekind’s Problem and beyond
Room B332 IBS (기초과학연구원)The Dedekind's Problem asks the number of monotone Boolean functions, a(n), on n variables. Equivalently, a(n) is the number of antichains in the n-dimensional Boolean lattice $^n$. While the exact …
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Matthew Kroeker, Average flat-size in complex-representable matroids
Room B332 IBS (기초과학연구원)Melchior’s Inequality (1941) implies that, in a rank-3 real-representable matroid, the average number of points in a line is less than three. This was extended to the complex-representable matroids by …
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Zichao Dong, Convex polytopes in non-elongated point sets in $\mathbb{R}^d$
Room B332 IBS (기초과학연구원)For any finite point set $P \subset \mathbb{R}^d$, we denote by $\text{diam}(P)$ the ratio of the largest to the smallest distances between pairs of points in $P$. Let $c_{d, \alpha}(n)$ …
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Ander Lamaison, Uniform Turán density beyond 3-graphs
Room B332 IBS (기초과학연구원)The uniform Turán density $\pi_u(F)$ of a hypergraph $F$, introduced by Erdős and Sós, is the smallest value of $d$ such that any hypergraph $H$ where all linear-sized subsets of …
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Sebastian Wiederrecht, Packing even directed circuits quarter-integrally
Room B332 IBS (기초과학연구원)We prove the existence of a computable function $f\colon\mathbb{N}\to\mathbb{N}$ such that for every integer $k$ and every digraph $D$ either contains a collection $\mathcal{C}$ of $k$ directed cycles of even …
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Jie Han (韩杰), Perfect matchings in dense uniform hypergraphs
Room B332 IBS (기초과학연구원)There has been a raising interest on the study of perfect matchings in uniform hypergraphs in the past two decades, including extremal problems and their algorithmic versions. I will introduce …
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Linda Cook, On polynomial degree-boundedness
Room B332 IBS (기초과학연구원)We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, and Walczak, that for every graph $H$, there is a polynomial $p$ such that for every positive integer $s$, every …