9,816 reputation
13124207
bio website gilkalai.wordpress.com
location Jerusalem
age 59
visits member for 5 years, 10 months
seen 16 mins ago
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Jan
5
revised Fundamental Examples
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Jan
5
revised Fundamental Examples
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Jan
2
comment Simplicial and cubical decompositions of low valence
Dear Dimitri, unfortunately I cannot answer your precise question and also I dont have a clear intuition what the answer should be. Regarding cubical structure and your conjecture I wonder if already the n dimensional torus can have a cubical structure where the degree of every vertex is less than 2^d.
Jan
2
answered Simplicial and cubical decompositions of low valence
Jan
1
comment How unhelpful is graph minors theorem?
Cant we test quickly if a graph is embeddable in a surface of genus 5 (say)?
Dec
31
comment What does the typical non-solvable group look like?
I think there is a large literature on enumeration of groups and it can be a very delicate matter. (It make a big difference, of course, if you rely on the classification.) It is true that for the specific question Noah asked it is even possible that direct product of A_5 with a typical group is typical. But i think there may be some versions of the question for which the answers will be even more interesting. E.g. if you do not allow any cyclic composition factors.
Dec
29
comment Algorithm or theory of diagram chasing
Is there a computer program for creating chasing-diagram proofs? E.g. for proving the five lemma en.wikipedia.org/wiki/Five_lemma. (I realize now it is a very special case of the Salamander lemma, but maybe a place to start thinking about it.) It looks that the type of arguments in a proof can be automotize somehow. Even if without any "actual" theory (I am not sure this is precisely what Greg has in mind. Anyway, maybe Doron Z. can be consulted.)
Dec
29
comment Poincaré quasi-isomorphism
Dear Nikolai, maybe the geometric (and rather explicit) description of duality for intersection homology in Goresky and McPherson paper (in Topology, 1980) can be useful for your purposes?
Dec
28
comment Algorithm or theory of diagram chasing
Very nice problem!
Dec
28
revised The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
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Dec
28
comment randomness in nature
Hi Kevin, I regard the question about the foundations of probability as important in mathematics as the question of the foundations of quantum mechanics is important in physics (and mathematics). It is true that there are various offered answers, and that there are philosophical aspects to the questions. Liza's question about randomness is similar in spirit but is more to my taste than say the question on Poincare conjecure and the shape of the universe (which nevertheless produced good answers). mathoverflow.net/questions/9708/…
Dec
27
revised randomness in nature
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Dec
27
comment randomness in nature
More answers, some discussion, are welcome here: gilkalai.wordpress.com/2009/12/27/randomness-in-nature
Dec
27
revised randomness in nature
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Dec
26
comment The shortest path in first passage percolation
Tom, Interseting suggestion. I dont remember so much what we tried. At the end we managed to go around this lemma.
Dec
26
comment The shortest path in first passage percolation
It may be possible that for this version (directed percolation; exponential lengths, maximum path), the detailed understanding of the model may lead to a proof of the lemma; but I am not sure even about it. (There are hopes, but no proofs for universality: that various models will behave in some sense the same way.) Strangely, I dont know the answer for a) off-hand. Nice question.
Dec
26
comment The shortest path in first passage percolation
Joe, it is a very good idea to consider paths from (0,0) to (n,n) and to consider also the case where you only go north and east. This restricted model is called "directed percolation". As far as I know the lemma is not known for directed percolation. There is one version where the distribution of edge length is exponential and you want the path of MAXIMUM length where this model is understood very well and is strongly connected to maximum eigenvalues of random symmetric matrices, largest monotone subsequences etc.
Dec
25
revised What exactly is the relationship between codes over finite fields and Euclidean sphere-packings?
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Dec
25
accepted Generalizations of Planar Graphs
Dec
25
accepted What precisely Is “Categorification”?