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Tag Archives: Helly type theorems
News on Fractional Helly, Colorful Helly, and Radon
My 1983 Ph D thesis was on Helly-type theorems which is an exciting part of discrete geometry and, in the last two decades, I have had an ongoing research project with Roy Meshulam on topological Helly-type theorems. The subject found … Continue reading
Basic Notions Seminar is Back! Helly Type Theorems and the Cascade Conjecture
Kazhdan’s Basic Notion Seminar is back! The “basic notion seminar” is an initiative of David Kazhdan who joined the Hebrew University math department around 2000. People give series of lectures about basic mathematics (or not so basic at times). Usually, speakers do … Continue reading
Posted in Combinatorics, Convexity, Open problems
Tagged David Kazhdan, Helly type theorems, Tverberg's theorem
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Colorful Caratheodory Revisited
Janos Pach wrote me: “I saw that you several times returned to the colored Caratheodory and Helly theorems and related stuff, so I thought that you may be interested in the enclosed paper by Holmsen, Tverberg and me, in … Continue reading
Sarkaria’s Proof of Tverberg’s Theorem 1
Helge Tverberg Ladies and gentlemen, this is an excellent time to tell you about the beautiful theorem of Tverberg and the startling proof of Sarkaria to Tverberg’s theorem (two parts). A good place to start is Radon’s theorem. 1. The theorems of Radon, … Continue reading
Helly’s Theorem, “Hypertrees”, and Strange Enumeration II: The Formula
In the first part of this post we discussed an appealing conjecture regaring an extension of Cayley’s counting trees formula. The number of d-dimensional “hypertrees” should somehow add up to . But it was not clear to us which complexes we want … Continue reading
Posted in Combinatorics, Convexity
Tagged Cayley theorem, Helly type theorems, Topological combinatorics
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