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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20220101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20231204T163000
DTEND;TZID=Asia/Seoul:20231204T173000
DTSTAMP:20260418T160236
CREATED:20231127T150526Z
LAST-MODIFIED:20240707T072633Z
UID:7951-1701707400-1701711000@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Almost spanning distance trees in subsets of finite vector spaces
DESCRIPTION: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 defined to be $\sum_{i=1}^d (x_i-y_i)^2$. An influential result of Iosevich and Rudnev is: if $E \subset \mathbb{F}_q^d$ is sufficiently large and $t \in \mathbb{F}_q$\, then there are a pair of points $x\,y \in E$ such that the distance between $x$ and $y$ is $t$. Subsequent works considered embedding graphs of distances\, rather than a single distance. I will discuss joint work with Debsoumya Chakraborti\, in which we show that every sufficiently large subset of $\mathbb{F}_q^d$ contains every nearly spanning tree of distances with bounded degree in each distance. The main novelty in this result is that the distance graphs we find are nearly as large as the set $S$ itself\, but even for smaller distance trees our work leads to quantitative improvements to previously known bounds. A key ingredient in our proof is a new colorful generalization of a classical result of Haxell on finding nearly spanning bounded-degree trees in expander graphs. This is joint work with Debsoumya Chakraborti.
URL:https://dimag.ibs.re.kr/event/2023-12-04/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20231212T163000
DTEND;TZID=Asia/Seoul:20231212T173000
DTSTAMP:20260418T160236
CREATED:20231019T075456Z
LAST-MODIFIED:20240707T072622Z
UID:7777-1702398600-1702402200@dimag.ibs.re.kr
SUMMARY:Ting-Wei Chao (趙庭偉)\, Tight Bound on Joints Problem and Partial Shadow Problem
DESCRIPTION: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 $O(N^{3/2})$ joints in $\mathbb R^3$ via the polynomial method. \nYu and I proved a tight bound on this problem\, which also solves a conjecture proposed by Bollobás and Eccles on the partial shadow problem. It is surprising to us that the only known proof of this purely extremal graph theoretic problem uses incidence geometry and the polynomial method.
URL:https://dimag.ibs.re.kr/event/2023-12-12/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20231219T163000
DTEND;TZID=Asia/Seoul:20231219T173000
DTSTAMP:20260418T160236
CREATED:20231015T221647Z
LAST-MODIFIED:20240707T072612Z
UID:7757-1703003400-1703007000@dimag.ibs.re.kr
SUMMARY:Shengtong Zhang (张盛桐)\, Triangle Ramsey numbers of complete graphs
DESCRIPTION: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 of copies of $F$ in a graph which is $H$-Ramsey. This generalizes the Ramsey number and size Ramsey number of a graph. Addressing a question of Spiro\, we prove that \[r_{K_3}(K_t)=\binom{r(K_t)}3\] for all sufficiently large $t$.  Our proof involves a combination of results on the chromatic number of triangle-sparse graphs. \nJoint work with Jacob Fox and Jonathan Tidor.
URL:https://dimag.ibs.re.kr/event/2023-12-19/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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