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Gil Kalai, The Cascade Conjecture and other Helly-type Problems

May 19 Thursday @ 4:15 PM - 5:15 PM KST

Zoom ID: 868 7549 9085

Speaker

[Colloquium, Department of Mathematical Sciences, KAIST]

For a set $X$ of points $x(1)$, $x(2)$, $\ldots$, $x(n)$ in some real vector space $V$ we denote by $T(X,r)$ the set of points in $X$ that belong to the convex hulls of r pairwise disjoint subsets of $X$.
We let $t(X,r)=1+\dim(T(X,r))$.

Radon’s theorem asserts that
If $t(X,1)< |X|$, then $t(X, 2) >0$.

The first open case of the cascade conjecture asserts that
If $t(X,1)+t(X,2) < |X|$, then $t(X,3) >0$.

In the lecture, I will discuss connections with topology and with various problems in graph theory. I will also mention questions regarding dimensions of intersection of convex sets.

Some related material:
1) A lecture (from 1999): An invitation to Tverberg Theorem: https://youtu.be/Wjg1_QwjUos
2) A paper on Helly type problems by Barany and me https://arxiv.org/abs/2108.08804
3) A link to Barany’s book: Combinatorial convexity https://www.amazon.com/Combinatorial-Convexity-University-Lecture-77/dp/1470467097

Details

Date:
May 19 Thursday
Time:
4:15 PM - 5:15 PM KST
Event Category:
Event Tags:
Website:
https://mathsci.kaist.ac.kr/home/schedules/seminar/?idx=-2736#heading-2736

Venue

Zoom ID: 868 7549 9085

Organizer

Andreas Holmsen
View Organizer Website
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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