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11106192
bio website gilkalai.wordpress.com
location Jerusalem
age 58
visits member for 4 years, 8 months
seen 21 hours ago
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Nov
29
awarded  Civic Duty
Nov
29
comment How Does Random Noise Typically Look?
Hmm, this looks convincing and the moment map argument is especially nice.
Nov
29
awarded  Popular Question
Nov
29
comment Why are planar graphs so exceptional?
I dont know if duality is behind everything but it is certainly behind many things. For example, consider 3-connected graphs. When we have such a planar graph the 2-cells are determined uniquely. (A theorem of Whiteney asserts that an induced cycle is a 2-face iff it is non seperating. On the other hand consider for example the polyhedral cell complex realizing the real projectice plane obtained by identifying opposite faces of the dodecahedron. The graph is the Petersen graph. The cells are not determined by the graph: Comparing the automorphism groups of the graph and of the 2-dim complex.
Nov
29
comment Why are planar graphs so exceptional?
One important manifestation of the uniqueness of planar graphs is Kasteleyn's formulas for the number of perfect matching and the connection with counting trees. Another geometric description (related to the relation with polytopes) is the Koebe-Andreev-Thurston theorem that allows to represent every planar graph by the "touching graph" of nonoverlapping circles.
Nov
29
revised Why are planar graphs so exceptional?
added 296 characters in body
Nov
29
answered Why are planar graphs so exceptional?
Nov
28
comment The inverse Galois problem, what is it good for?
I also agree. In fact, the problem is more natural than other famous open problems so it is an obvious challenge mathematicians face and progress in mathematics measured. There are views (see ihes.fr/~gromov/topics/SpacesandQuestions.pdf ) that dismiss the importance of "natural" problems rather than deep emerging problems. But even if you agree to this opinion (and I tend not to agree) Natural old-standing problems stand as an objective measure for progress in math.
Nov
28
comment k-pseudorandom measures
Maybe this post from "in theory" lucatrevisan.wordpress.com/2008/06/05/… is relevant
Nov
28
comment How to think about CM rings?
Any links for Serre's S_n properties? Does CM mean to have property S_i for every i?
Nov
28
revised How to think about CM rings?
spelling
Nov
28
revised The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
unite two tags
Nov
28
comment When shorter means smaller?
Do sets of constant width have this property?
Nov
28
answered Fundamental Examples
Nov
28
answered Fundamental Examples
Nov
28
comment Is there a matrix whose permanent counts 3-colorings?
Harrison, the fact that 3-coloring is #P does not mean that there is a description of the number of 3-coloring of a graph as a permanent.
Nov
27
comment Is there a theorem that says that there is always more than one way to “continue a finite sequence”?
I like the question and it led to 8 nice answers
Nov
27
comment Fundamental Examples
This great answer have earned Charles the first gold badge in mathoverflow history. Congratulations, Charles!
Nov
27
revised Fundamental Examples
chane "is" to "was"
Nov
27
comment Generalizations of the Birkhoff-von Neumann Theorem
Actually the motivation for the question is a recent extension of the Birkhoff-von Neumann theorem by Ellis, Friedgut and Pilpel that I heard yeasterday. I thought it can be useful to try to collect various such generalizations fron various directions and it is also true that Greg and I discussed over the years no less than three different directions where this theorem is extended on of which is the "non-generalization" Greg's mention. (Greg, is there any reference or link?) (In any case, what is "cheating" about it?)