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Recent Posts
 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 TelAviv
 Oded Goldreich Fest
 The Race to Quantum Technologies and Quantum Computers (Useful Links)
 Around the GarsiaStanley’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
 The Race to Quantum Technologies and Quantum Computers (Useful Links)
 Call for nominations for the Ostrowski Prize 2017
 Believing that the Earth is Round When it Matters
 Extremal Combinatorics VI: The FranklWilson Theorem
 Updates and plans III.
 Can Category Theory Serve as the Foundation of Mathematics?
 A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
 Happy Birthday Ron Aharoni!
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Category Archives: Open problems
Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota’s Conjecture on Matroids
Gian Carlo Rota Rota’s conjecture I just saw in the Notices of the AMS a paper by Geelen, Gerards, and Whittle where they announce and give a high level description of their recent proof of Rota’s conjecture. The 1970 conjecture asserts … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Bert Gerards, Eric Katz, Geoﬀ Whittle, Gian Carlo Rota, Jim Geelen, June Huh, Matroids
7 Comments
My Mathematical Dialogue with Jürgen Eckhoff
Jürgen Eckhoff, Ascona 1999 Jürgen Eckhoff is a German mathematician working in the areas of convexity and combinatorics. Our mathematical paths have met a remarkable number of times. We also met quite a few times in person since our first … Continue reading
Posted in Combinatorics, Convex polytopes, Open problems
Tagged Andy Frohmader, Helly's theorem, Jurgen Eckhoff, Nina Amenta, Noga Alon, Roy Meshulam
1 Comment
NavierStokes Fluid Computers
Smart fluid Terry Tao posted a very intriguing post on the NavierStokes equation, based on a recently uploaded paper Finite time blowup for an averaged threedimensional NavierStokes equation. The paper proved a remarkable negative answer for the regularity conjecture for a certain … Continue reading
Amazing: Peter Keevash Constructed General Steiner Systems and Designs
Here is one of the central and oldest problems in combinatorics: Problem: Can you find a collection S of qsubsets from an nelement set X set so that every rsubset of X is included in precisely λ sets in the collection? … Continue reading
Many triangulated threespheres!
The news Eran Nevo and Stedman Wilson have constructed triangulations with n vertices of the 3dimensional sphere! This settled an old problem which stood open for several decades. Here is a link to their paper How many nvertex triangulations does the 3 … Continue reading
Posted in Combinatorics, Convex polytopes, Geometry, Open problems
Tagged Eran Nevo, Stedman Wilson
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Polymath 8 – a Success!
Yitang Zhang Update (July 22, ’14). The polymath8b paper “Variants of the Selberg sieve, and bounded intervals containing many primes“, is now on the arXiv. See also this post on Terry Tao’s blog. Since the last update, we also had here … Continue reading
Around Borsuk’s Conjecture 3: How to Save Borsuk’s conjecture
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
Poznań: Random Structures and Algorithms 2013
Michal Karonski (left) who built Poland’s probabilistic combinatorics group at Poznań, and a sculpture honoring the Polish mathematicians who first broke the Enigma machine (right, with David Conlon, picture taken by Jacob Fox). Update: Here is a picture from 2015, while … Continue reading
Posted in Combinatorics, Conferences, Open problems, Philosophy, Probability
Tagged Poznan, RSA
2 Comments
Some old and new problems in combinatorics and geometry
Paul Erdős in Jerusalem, 1933 1993 Update: Here is a link to a draft of a paper* based on the first part of this lecture. Some old and new problems in combinatorial geometry I: Around Borsuk’s problem. I just came back from … Continue reading
Andriy Bondarenko Showed that Borsuk’s Conjecture is False for Dimensions Greater Than 65!
The news in brief Andriy V. Bondarenko proved in his remarkable paper The Borsuk Conjecture for twodistance sets that the Borsuk’s conjecture is false for all dimensions greater than 65. This is a substantial improvement of the earlier record (all dimensions … Continue reading