9,606 reputation
13119202
bio website gilkalai.wordpress.com
location Jerusalem
age 59
visits member for 5 years, 8 months
seen 1 hour ago
Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

1h
comment What are some good short statements that attempt to define mathematics?
I propose that the question will be limited to thoughtful definitions that those who give them actually endorse (and if not their own give reference to) and not for a board list of all fewer than 30 words definition in existence.
May
5
comment Logic in mathematics and philosophy
No, make that the end of the 18th century.
Apr
30
comment Models for graphs representing real-life networks
Dear Rupei, Thanks a lot
Apr
28
comment Models for graphs representing real-life networks
It is a nice answer, Joe, Thanks!
Apr
28
comment Models for graphs representing real-life networks
I am interested (at this point) in the graphs themselves.
Apr
12
comment Intersecting Family of Triangulations
Dear Bruno, thanks very nice!
Apr
5
comment 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
comment 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
comment 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
comment 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
comment Primes and Parity
Thanks, Stopple (corrected) and Lucia
Dec
2
comment Bounding the absolute sum of entries of the inverse of a 0-1 matrix
(belated) Welcome to MO, Noga!
Dec
2
comment 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
comment 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
comment Stable matchings when switches have costs
Very nice question!!
Jul
9
comment Solutions to the Continuum Hypothesis
Asaf, ok I will delete it.
May
23
comment 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
comment 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
comment 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
comment 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?