# Tag Archives: Tverberg’s theorem

## 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

## Attila Por’s Universality Result for Tverberg Partitions

In this post  I would like to tell you about three papers and three theorems. I am thankful to Moshe White and Imre Barany for helpful discussions. a) Universality of vector sequences and universality of Tverberg partitions, by Attila Por; Theorem … 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 | | 4 Comments

## Seven Problems Around Tverberg’s Theorem

Imre Barany, Rade Zivaljevic, Helge Tverberg, and Sinisa Vrecica  Recall the beautiful theorem of Tverberg: (We devoted two posts (I, II) to its background and proof.) Tverberg Theorem (1965): Let be points in , . Then there is a partition of … Continue reading

## Sarkaria’s Proof of Tverberg’s Theorem 2

Karanbir Sarkaria 4. Sarkaria’s proof: Tverberg’s theorem (1965): Let be points in , . Then there is a partition of such that . Proof: We can assume that . First suppose that the points belong to the -dimensional affine space in … Continue reading

Posted in Convexity | | 13 Comments

## 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

Posted in Convexity | | 18 Comments