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- To cheer you up in difficult times 32, Annika Heckel's guest post: How does the Chromatic Number of a Random Graph Vary?
- To cheer you up in difficult times 11: Immortal Songs by Sabine Hossenfelder and by Tom Lehrer
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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
4 Comments

## 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
6 Comments