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 Polymath10post 4: Back to the drawing board?
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 Polymath10, Post 2: Homological Approach
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 Convex Polytopes: Seperation, Expansion, Chordality, and Approximations of Smooth Bodies
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 Polymath10post 4: Back to the drawing board?
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Believing that the Earth is Round When it Matters
 News (mainly polymath related)
 The KadisonSinger Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
 Polymath10: The Erdos Rado Delta System Conjecture
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 Polymath 10 Post 3: How are we doing?
 Midrasha Mathematicae #18: In And Around Combinatorics
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Category Archives: Open problems
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
New Ramanujan Graphs!
Margulis’ paper Ramanujan graphs were constructed independently by Margulis and by Lubotzky, Philips and Sarnak (who also coined the name). The picture above shows Margulis’ paper where the graphs are defined and their girth is studied. (I will come back to the question … Continue reading
Posted in Algebra and Number Theory, Combinatorics, Open problems
Tagged Ramanujan graphs
10 Comments
A Few Mathematical Snapshots from India (ICM2010)
Can you find Assaf in this picture? (Picture: Guy Kindler.) In my post about ICM 2010 and India I hardly mentioned any mathematics. So here are a couple of mathematical snapshots from India. Not so much from the lectures themselves but … Continue reading
Posted in Conferences, Open problems
Tagged Assaf Naor, Eric Rains, François Loeser, Günter Ziegler, ICM2010
1 Comment
Looking Again at Erdős’ Discrepancy Problem
Over Gowers’s blog Tim and I will make an attempt to revisit polymath5. Last Autumn I prepared three posts on the problems and we decided to launch them now. The first post is here. Here is a related MathOverflow question. … Continue reading
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