- 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
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Believing that the Earth is Round When it Matters
- In how many ways you can chose a committee of three students from a class of ten students?
- Amazing: Peter Keevash Constructed General Steiner Systems and Designs
- A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
- Answer To Test Your Intuition (4)
- Some old and new problems in combinatorics and geometry
- Extremal Combinatorics VI: The Frankl-Wilson Theorem
Category Archives: Open problems
On June 18-23 2017 we will celebrate in Budapest the 70th birthday of Imre Bárány. Here is the webpage of the conference. For the occasion I wrote a short paper with problems in discrete geometry, mainly around Helly’s and … Continue reading
The Ramsey numbers R(s,t) The Ramsey number R(s, t) is defined to be the smallest n such that every graph of order n contains either a clique of s vertices or an independent set of t vertices. Understanding the values … Continue reading
On the occasion of Polymath 12 devoted to the Rota basis conjecture let me remind you about the Alon-Tarsi conjecture and test your intuition concerning a strong form of the conjecture. The sign of a Latin square is the product … Continue reading
The Polymath10 project on the Erdos-Rado Delta-System conjecture took place over this blog from November 2015 to May 2016. I aimed for an easy-going project that people could participate calmly aside from their main research efforts and the duration of … Continue reading
Polymath 10 post 6: The Erdos-Rado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
In earlier posts I proposed a homological approach to the Erdos-Rado sunflower conjecture. I will describe again this approach in the second part of this post. Of course, discussion of other avenues for the study of the conjecture are welcome. The purpose … Continue reading
Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
A quote from a recent post from Jordan Ellenberg‘s blog Quomodocumque: Briefly: it seems to me that the idea of the Croot-Lev-Pach paper I posted about yesterday (GK: see also my last post) can indeed be used to give a new bound … Continue reading
This post is authored by Stefan Steinerberger. The Ulam sequence is defined by starting with 1,2 and then repeatedly adding the smallest integer that is (1) larger than the last element and (2) can be written as the sum of two … Continue reading
The main purpose of this post is to start a new research thread for Polymath 10 dealing with the Erdos-Rado Sunflower problem. (Here are links to post 2 and post 1.) Here is a very quick review of where we … Continue reading
Readers of the big-league ToC blogs have already heard about the breakthrough paper An average-case depth hierarchy theorem for Boolean circuits by Benjamin Rossman, Rocco Servedio, and Li-Yang Tan. Here are blog reports on Computational complexity, on the Shtetl Optimized, and of Godel … Continue reading
Coloring Edge-coloring of simple polytopes One of the equivalent formulation of the four-color theorem asserts that: Theorem (4CT) : Every cubic bridgeless planar graph is 3-edge colorable So we can color the edges by three colors such that every two … Continue reading