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 Media Item from “Haaretz” Today: “For the first time ever…”
 Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota’s Conjecture on Matroids
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 Next Week in Jerusalem: Special Day on Quantum PCP, Quantum Codes, Simplicial Complexes and Locally Testable Codes
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 Believing that the Earth is Round When it Matters
 The KadisonSinger Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 A Few Mathematical Snapshots from India (ICM2010)
 Why Quantum Computers Cannot Work: The Movie!
 Two Math Riddles
 Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota's Conjecture on Matroids
 Media Item from "Haaretz" Today: "For the first time ever..."
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Category Archives: Open problems
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
Cup 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