bio | website | gilkalai.wordpress.com |
---|---|---|

location | Jerusalem | |

age | 59 | |

visits | member for | 5 years, 5 months |

seen | 2 hours ago | |

stats | profile views | 17,769 |

Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Apr 12 |
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Intersecting Family of Triangulations
Dear Bruno, thanks very nice! |

Apr 5 |
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Enumeration of $0-1$ matrices with determinant $1$
Regarding det (A) behaving uniformly below the value $n^{n/2}$ there is a heuristic which slightly corrects it (but it looks that it will not make a difference regarding the $2^{n^2-O(n\log n)}$ estimate. The heuristic is that mod a prime the determinant of A behaves like that of a random matrix modulo p. This gives some guess regarding ,e.g., $prob (det (A)=2) /Prob (det (A)=1). |

Apr 5 |
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Enumeration of $0-1$ matrices with determinant $1$
There are several heuristic arguments for the asymptotic of f(n) which unfortunately gives different answers. Probably I would vote against the idea that upper unitriangular matrices gives most contribution. There are pretty good results and even better conjectures for the number of matrices with determinant 0. This occurse (conjecturaly) mainly if a row (column) is zero or two rows (columns) agree which gives 2^n^2 / n^2 2^n. This suggests that f(n) is also at most 2^n^2/c^n. It is reasonable to believe that det (A) is pretty close to being uniform below n^n/2 which justifies Noam's guess. |

Feb 19 |
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The amplituhedron minus the physics
I meant that the matrix representing the projection is totally positive (all minors are positive). It is enough that all maximal minors are positive. |

Feb 12 |
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Primes and Parity
Dear Mark, my highly uneducated guess would be that just based on density (or even on other known properties or even on RH) you want be able to find a small collection of such AP's. |

Jan 31 |
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Primes and Parity
Thanks, Stopple (corrected) and Lucia |

Dec 2 |
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Bounding the absolute sum of entries of the inverse of a 0-1 matrix
(belated) Welcome to MO, Noga! |

Dec 2 |
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lower-bound for $Pr[X\geq EX]$
Dear Fedja, This is a very nice proof, and especially the new nice trick to pass to exp (2Y) and what follows. As Ryan mentioned there is a nice conjecture by Uri Feige (in the paper) that the best bound is obtained when each of the n variables is n+1 with probability 1/(n+1). |

Sep 27 |
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Characterizing faces of 3-dimensional polyhedra. (Related to Victor Eberhard's Theorem [1890]:)
Dear Kundor, as it turned out the question remains open. (I forgot to update.) |

Jul 26 |
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Stable matchings when switches have costs
Very nice question!! |

Jul 9 |
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Solutions to the Continuum Hypothesis
Asaf, ok I will delete it. |

May 23 |
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Examples of graph properties characterized by forbidden (not necessarily induced) subgraphs
In the case of graphs on surfaces we get a finite list of graphs so that a graph which is cannot be embedded must contain a subdivision of a graph from the list. |

May 2 |
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How to find ICM talks?
Quid, beside ICM and ECM what are other major congresses/conferences with major proceedings that we can ask about? (I could think also of INTERNATIONAL CONGRESS OF MATHEMATICAL PHYSICS (ICMP)), I am worry that a completely open-ended question will not be so useful without careful management. |

May 1 |
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How to find ICM talks?
I am not sure about asking and answering my own question as you suggested, Quid. If you want to ask this, or a more general question, I will be happy to answer. Meanwhile it can be a nice supplement here. |

Apr 30 |
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Grassmann-Plücker relations for permanents
Dear Abdelmalek, many thanks for the answer. You wrote "Set theoretic equations (of degree d+1) were discovered by Brill and Gordan." Can you elaborate on these equations? |

Apr 29 |
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A question about pairs of lines in 3D projective space
Amazing!! Many thanks, David. Very nice result. |

Apr 28 |
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A question about pairs of lines in 3D projective space
Thanks, David. Yes this is correct. But we can identify the quaternions with 2 dimensional v.s. over the complex so we get 8 choose 4. and then we can save a bit by intersecting with a generic hyperplane and get 7 choose 3. I wonder if Amitsur's theorem is relevant. |

Apr 28 |
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A question about pairs of lines in 3D projective space
The following MO question is of some relevance mathoverflow.net/questions/65421/… |

Apr 24 |
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Why was John Nash's 1950 Game Theory paper such a big deal?
Joël, Of course there are also issues with the notion of value for zero-sum 2-person games, like the need to have mixed strategies which is problematic in various cases (and various others issues). Once you apply Von Neumann and Morgenstern utility theory on mixed outcomes you often loose the zero-sum property. But I agree that the notion of a value of zero-sum games is also very important. |

Apr 23 |
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Why was John Nash's 1950 Game Theory paper such a big deal?
Dear Joël, I agree. To a large extent Nash equilibrium is a miracle concept leading to (almost) all the problems in applied game theory. It often represents genuine problems and shortcomings not only of economics theory but also of economics reality. Certainly this is something we, as mathematicians can celebrate and be enthusiastic about! |