James Davies, Odd distances in colourings of the plane
Room B332 IBS (기초과학연구원)We prove that every finite colouring of the plane contains a monochromatic pair of points at an odd integral distance from each other.
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Seminars and Colloquiums
Bruce A. Reed, Some Variants of the Erdős-Sós Conjecture
Room B332 IBS (기초과학연구원)Determining the density required to ensure that a host graph G contains some target graph as a subgraph or minor is a natural and well-studied question in extremal combinatorics. The …
Seunghun Lee (이승훈), On colorings of hypergraphs embeddable in $\mathbb{R}^d$
Room B332 IBS (기초과학연구원)Given a hypergraph $H=(V,E)$, we say that $H$ is (weakly) $m$-colorable if there is a coloring $c:V\to $ such that every hyperedge of $H$ is not monochromatic. The (weak) chromatic …
Hyunwoo Lee (이현우), Towards a high-dimensional Dirac’s theorem
Room B332 IBS (기초과학연구원)Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger …
Ben Lund, Almost spanning distance trees in subsets of finite vector spaces
Room B332 IBS (기초과학연구원)For $d\ge 2$ and an odd prime power $q$, let $\mathbb{F}_q^d$ be the $d$-dimensional vector space over the finite field $\mathbb{F}_q$. The distance between two points $(x_1,\ldots,x_d)$ and $(y_1,\ldots,y_d)$ is …
Ting-Wei Chao (趙庭偉), Tight Bound on Joints Problem and Partial Shadow Problem
Room B332 IBS (기초과학연구원)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 …
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 …
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 …
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 …
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 …