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bio website gilkalai.wordpress.com
location Jerusalem
age 59
visits member for 5 years, 8 months
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Professor of Mathematics at the Hebrew University of Jerusalem and at Yale University

Apr
28
asked Models for graphs representing real-life networks
Apr
16
awarded  Good Answer
Apr
14
awarded  Good Answer
Apr
13
revised Fundamental Examples
added 31 characters in body
Apr
12
awarded  Favorite Question
Apr
12
revised Intersecting Family of Triangulations
added 195 characters in body
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.
Apr
4
revised f(f(x))=exp(x)-1 and other functions “just in the middle” between linear and exponential
added 84 characters in body
Mar
12
awarded  Nice Answer
Mar
11
answered Logic in mathematics and philosophy
Mar
3
awarded  Good Answer
Feb
28
revised f(f(x))=exp(x)-1 and other functions “just in the middle” between linear and exponential
added 167 characters in body; edited title
Feb
28
answered Experimental Mathematics
Feb
28
revised Logic in mathematics and philosophy
added 128 characters in body
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
18
revised The amplituhedron minus the physics
added 340 characters in body
Feb
18
revised What is the amplituhedron?
added 289 characters in body
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.