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bio website gilkalai.wordpress.com
location Jerusalem
age 59
visits member for 5 years, 1 month
seen Dec 14 at 21:56
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Nov
22
comment Theorems for nothing (and the proofs for free)
Indeed this is a wonderful theorem. Why is it intuitive correct? From all the first year algebra theorems it was the one where I had no intuition whatsoever.
Nov
22
revised The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
added 184 characters in body
Nov
22
comment Fundamental Examples
Kevin guys, the bounty is meant to encourage further answers.
Nov
22
comment The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
The Gallai Sylvester theorem is precisely about non generic variety and non generic flat intersecting it.
Nov
21
revised A “round” lattice with low kissing number?
added 1398 characters in body
Nov
21
comment Fundamental Examples
yes, perhaps along with nim.
Nov
21
comment Fundamental Examples
(...and cluster algeras) This is definitely a good example.
Nov
21
comment The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
Well, even in the original high dimensional generalization of Gallai Sylvester to have the simplest intersection with k-flat you need the ambient space be 2k-dimensional. Also for the conjectured generalization we need the abmient space be large. Now, k-faces of n-polytopes cannot be too complicated when n is large. (Or at least, so we believe).For example, n-polytopes always have 2-faces which are triangles of quadrangles. I do not see how an example like the one suggested in the answer works when the ambient space is high dimensional.
Nov
21
asked What is an integrable system
Nov
21
revised Fundamental Examples
added 167 characters in body
Nov
21
accepted The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
Nov
21
comment The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
In any case Greg's answer pushed the problem enough to be accepted. More answers are nevertheless welcome.
Nov
21
comment The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
I do not see yet how the example [or such an example] allows 1-dimensional intersection of a 3-planes [ot 2-plane] with V with arbitrary complicated topology, when the abbient space is of high dimension. It looks that indeed it shows that for 1-dimensional intersection with a 3-plane for a variety in 4 space, the topology cannot be as tight as in the original G-S thm. (Unbounded number of connected components seems anavidable.) I dont see if in this example the topology can be arbitrary complicated. I'll be happy to hear more on the last paragraph. (several constructions and open-ended probs)
Nov
21
comment The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
This is an excellent answer and let me give some more detailes about it. First, it raises interesting special cases and generalizations of the problem. 1. Certainly a case which deserves to be singled out is the case where V comes from an arrangelemt of subspaces. I.e., when V is the union of affine subspaces of an n-dimensional space. (The original case deals with 0-subspaces.) 2. It suggests to study the problem (in the real case) for semi-algebraic varieties. Those include sets like skeleta of polytopes and skeleta with added diagonals. 3. To consider smooth varieties.
Nov
21
comment Combinatorics of the Stasheff polytopes
The Stasheff polytope is simple, right? so the number of edges is d/2 times the number of vertices, where d=n-3 is the dimension. I think there are formulas for all the face numbers.
Nov
21
comment Super-linear time complexity lower bounds for any natural problem in NP?
Here is a citation and a link : Uri Zwick, A 4n lower bound on the combinatorial complexity of certain symmetric Boolean functions over the basis of unate dyadic Boolean functions SIAM Journal on Computing 20, 499-505 (1991) An explicit lower bound of 5n-o (n) for boolean circuits, K Iwama, O. Lachish, H Morizumi, and R. Raz springerlink.com/index/XCP1TCRY1C236RDT.pdf The introduction of the second paper and the slow incremental improvements may give some idea on the difficulty of the problem.
Nov
21
revised Something like mathoverflow in other sciences
added 15 characters in body; edited tags
Nov
21
answered Theorems for nothing (and the proofs for free)
Nov
21
comment Theorems for nothing (and the proofs for free)
Here is a related discussion gilkalai.wordpress.com/2009/08/03/…
Nov
21
answered A single paper everyone should read?