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bio website gilkalai.wordpress.com
location Jerusalem
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Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Dec
2
answered What are the most overloaded words in mathematics?
Dec
1
revised Minkowski sum of small connected sets
edited tags
Dec
1
comment Why are planar graphs so exceptional?
That's interesting. I was not aware of it; So is the statement that every graph can be realized by a circle packing on arbitrary surface? (with a Riemannian metric?) Is there also uniqueness results like in the planar case?
Dec
1
comment Fundamental Examples
Is it possible? Is it moral?
Dec
1
answered Fundamental Examples
Dec
1
revised Why are planar graphs so exceptional?
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Dec
1
revised Why are planar graphs so exceptional?
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Dec
1
revised Why are planar graphs so exceptional?
added 3715 characters in body; added 41 characters in body
Nov
30
revised Fundamental Examples
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Nov
30
accepted How Does Random Noise Typically Look?
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?
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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?