Tag Archives: Tverberg’s theorem

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 , , | 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

Posted in Combinatorics, Convexity, Open problems | Tagged , , | 21 Comments

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 | Tagged , | 12 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 | Tagged , | 16 Comments