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Ting-Wei Chao (趙庭偉), Tight Bound on Joints Problem and Partial Shadow Problem

Tuesday, December 12, 2023 @ 4:30 PM - 5:30 PM KST

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 $O(N^{3/2})$ joints in $\mathbb R^3$ via the polynomial method.

Yu 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.


Tuesday, December 12, 2023
4:30 PM - 5:30 PM KST
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Room B332
IBS (기초과학연구원) + Google Map


Hong Liu
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IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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