bio | website | gilkalai.wordpress.com |
---|---|---|
location | Jerusalem | |
age | 59 | |
visits | member for | 5 years, 9 months |
seen | 14 mins ago | |
stats | profile views | 18,342 |
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University
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 |
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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 |
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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? |
Nov
21 |
comment |
The Sylvester Gallai Theorem and Sections of Varieties with “Simple Topology”.
Excellent answer, Greg, thanks. |
Nov
21 |
revised |
A single paper everyone should read?
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Nov
20 |
answered | A single paper everyone should read? |
Nov
20 |
comment |
Definition of “simplicial complex”
right, i meant 7 vertices... |
Nov
20 |
answered | Definition of “simplicial complex” |
Nov
20 |
comment |
Math Vs Social Science
This is very interesting, and Nate Silver looks like an extraordinary guy and certainly a good statistcian. (See also en.wikipedia.org/wiki/Nate_Silver .) Of course, we need to be cautios about this story and possible interpretations. (For example, quite a few academic statisticians are involved in polling planning and analysis and they probably are aware of graduate level statistics.) Also for role models of using mathematics in social sciences, I would still prefer the standard academic avenues of papers in professional journals etc. |
Nov
20 |
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How Does Random Noise Typically Look?
I agree that this is not realistic - neither in the quantum case neither in the classic case. (At least not without much further explanation.) I only asked about the factual matter: what is the situation in the classical case. It was strange for me that I do not know the answer (and not precisely the question) for a question which was easy in the quantum case. It is still not clear to me how to do the computation for a random stochastic map and what the answer is. |
Nov
20 |
comment |
How Does Random Noise Typically Look?
I did not fully understand the answer, but I like the thought. |