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Gil Kalai, The Cascade Conjecture and other Helly-type Problems
Thursday, May 19, 2022 @ 4:15 PM - 5:15 PM KST
[Colloquium, Department of Mathematical Sciences, KAIST]
For a set
We let
Radon’s theorem asserts that
If
The first open case of the cascade conjecture asserts that
If
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