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 Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
 Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
 More Math from Facebook
 The Erdős Szekeres polygon problem – Solved asymptotically by Andrew Suk.
 The Quantum Computer Puzzle @ Notices of the AMS
 Three Conferences: Joel Spencer, April 2930, Courant; Joel Hass May 2022, Berkeley, Jean Bourgain May 2124, IAS, Princeton
 Math and Physics Activities at HUJI
 Stefan Steinerberger: The Ulam Sequence
Top Posts & Pages
 Polymath 10 Emergency Post 5: The ErdosSzemeredi Sunflower Conjecture is Now Proven.
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
 Polymath 10 post 6: The ErdosRado sunflower conjecture, and the Turan (4,3) problem: homological approaches.
 Believing that the Earth is Round When it Matters
 Amazing: Peter Keevash Constructed General Steiner Systems and Designs
 The Erdős Szekeres polygon problem  Solved asymptotically by Andrew Suk.
 Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
 Polymath10: The Erdos Rado Delta System Conjecture
 Polymath10, Post 2: Homological Approach
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Category Archives: Open problems
A Weak Form of Borsuk Conjecture
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.
Satoshi Murai and Eran Nevo proved the Generalized Lower Bound Conjecture.
Satoshi Murai and Eran Nevo have just proved the 1971 generalized lower bound conjecture of McMullen and Walkup, in their paper On the generalized lower bound conjecture for polytopes and spheres . Let me tell you a little about it. … Continue reading
Cap Sets, Sunflowers, and Matrix Multiplication
This post follows a recent paper On sunflowers and matrix multiplication by Noga Alon, Amir Spilka, and Christopher Umens (ASU11) which rely on an earlier paper Grouptheoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading
Joe’s 100th MO question
MathOverflow is a remarkable recent platform for research level questions and answers in mathematics. Joe O’Rourke have asked over MO wonderful questions. (Here is a link to the questions) Many of those questions can be the starting point of a research … Continue reading
Posted in Mathematics over the Internet, Open problems
Tagged Joseph O'Rourke, Math Overflow, planetMO
4 Comments
A Couple Updates on the AdvancesinCombinatorics Updates
In a recent post I mentioned quite a few remarkable recent developments in combinatorics. Let me mention a couple more. Independent sets in regular graphs A challenging conjecture by Noga Alon and Jeff Kahn in graph theory was about the number of … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Independent sets in graphs, Roth's theorem
4 Comments
The Combinatorics of Cocycles and Borsuk’s Problem.
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
Is Backgammon in P?
The Complexity of ZeroSum Stochastic Games with Perfect Information Is there a polynomial time algorithm for chess? Well, if we consider the complexity of chess in terms of the board size then it is fair to think that the answer is … Continue reading
Polynomial Hirsch Conjecture 5: Abstractions and Counterexamples.
This is the 5th research thread of polymath3 studying the polynomial Hirsch conjecture. As you may remember, we are mainly interested in an abstract form of the problem about families of sets. (And a related version about families of multisets.) The … Continue reading
Roth’s Theorem: Tom Sanders Reaches the Logarithmic Barrier
Click here for the most recent polymath3 research thread. I missed Tom by a few minutes at MittagLeffler Institute a year and a half ago Suppose that is a subset of of maximum cardinality not containing an arithmetic progression of length 3. Let . … Continue reading
Posted in Combinatorics, Open problems
Tagged Endre Szemeredi, Jean Bourgain, Klaus Roth, Roger HeathBrown, Roth's theorem, Tom Sanders
9 Comments
János Pach: Guth and Katz’s Solution of Erdős’s Distinct Distances Problem
Click here for the most recent polymath3 research thread. Erdős and Pach celebrating another November day many years ago. The Wolf disguised as Little Red Riding Hood. Pach disguised as another Pach. This post is authored by János Pach A … Continue reading
Posted in Combinatorics, Geometry, Guest blogger, Open problems
Tagged Larry Guth, Nets Hawk Katz
13 Comments