- Call for nominations for the Ostrowski Prize 2017
- Problems for Imre Bárány’s Birthday!
- Twelves short videos about members of the Department of Mathematics and Statistics at the University of Victoria
- Jozsef Solymosi is Giving the 2017 Erdős Lectures in Discrete Mathematics and Theoretical Computer Science
- Updates (belated) Between New Haven, Jerusalem, and Tel-Aviv
- Oded Goldreich Fest
- The Race to Quantum Technologies and Quantum Computers (Useful Links)
- Around the Garsia-Stanley’s Partitioning Conjecture
- My Answer to TYI- 28
Top Posts & Pages
- Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
- Test your intuition 28: What is the most striking common feature to all these remarkable individuals
- Chess can be a Game of Luck
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Igor Pak's "Lectures on Discrete and Polyhedral Geometry"
- Important formulas in Combinatorics
- International mathematics graduate studies at the Hebrew University of Jerusalem
- Answer To Test Your Intuition (4)
- Francisco Santos Disproves the Hirsch Conjecture
Category Archives: Convexity
The topological Tverberg conjecture (discussed in this post), a holy grail of topological combinatorics, was refuted! The three-page paper “Counterexamples to the topological Tverberg conjecture” by Florian Frick gives a brilliant proof that the conjecture is false. The proof is … Continue reading
Borsuk asked in 1933 if every bounded set K of diameter 1 in can be covered by d+1 sets of smaller diameter. A positive answer was referred to as the “Borsuk Conjecture,” and it was disproved by Jeff Kahn and me in 1993. … Continue reading
Problem: Let P be a polytope in with n facets. Is it always true that P can be covered by n sets of smaller diameter? I also asked this question over mathoverflow, with some background and motivation.
Greetings to all! Karol Borsuk conjectured in 1933 that every bounded set in can be covered by sets of smaller diameter. In a previous post I described the counterexample found by Jeff Kahn and me. I will devote a few posts … Continue reading
Cocycles Definition: A -cocycle is a collection of -subsets such that every -set contains an even number of sets in the collection. Alternative definition: Start with a collection of -sets and consider all -sets that contain an odd number of members … Continue reading
Martin Tancer recently found a very beautiful proof that finite projective planes can’t be represented by convex sets in any fixed dimension. This was asked in the paper entitled “Transversal numbers for hypergraphs arising in geometry” by Noga Alon, Gil … Continue reading
Pavle Blagojevic, Benjamin Matschke, and Guenter Ziegler settled for the case that is a prime, the “colorful Tverberg’s conjecture.” (Problem 6 in this post.) This gives a sharp version for Zivaljevic and Vrecica theorem, and crossed the “connectivity of chessboard complexes barrier”. Here is … Continue reading
Here is a link to Igor Pak’s book on Discrete and Polyhedral Geometry (free download) . And here is just the table of contents. It is a wonderful book, full of gems, contains original look on many important directions, things that … Continue reading
Here is an answer to “Test your intuition (8)”. (Essentially the answer posed by David Eppstein.) (From Wolfram Mathworld) Buffon’s needle problem asks to find the probability that a needle of length will land on a line, given a floor … Continue reading