bio  website  math.mit.edu/~shor 

location  M.I.T., Cambridge, MA  
age  55  
visits  member for  5 years, 8 months 
seen  13 hours ago  
stats  profile views  6,918 
I'm a professor in the Mathematics Dept. at M.I.T. I mostly work on quantum computation, quantum information, and quantum complexity, but I am also interested in other areas of theoretical computer science and mathematics.
14h

comment 
Lower bounding the probability that $\gcd(t,N)≤B$, for a random $t$ and fixed (large) $N$
After seeing the proofs here, I'm not at all embarrassed that I didn't remember Odlyzko's proof (if the proof had been easy, I probably still wouldn't remember it, but I'd be embarrassed about it). 
Jul 17 
awarded  Good Answer 
May 10 
comment 
A claim from “Graph minors  a survey” by Robertson and Seymour
Isn't this straightforward induction? 
Jan 4 
comment 
Transforming a binary matrix into triangular form using permutation matrices
This just had an answer which got deleted. Here's a simplification of it (definitely based on it). (a) prove that any row with a single 1 can serve as the first row. (b) use the following algorithm: choose a row with a single 1 for the first row. Delete the column that 1 is in. Then recurse. How do you prove any row with a single 1 can serve as the first row? Consider an $n \times n$ matrix $M$ with $M(i,j) = 1$ if $j \leq i$ except for row $i'$, which has exactly one $1$ in position $(i',j')$ with $j' \leq i'$. Cyclically permute the rows from $1$ to $i'$, and the columns from $1$ to $j'$. 
Dec 10 
comment 
Can we cover the unit square by these rectangles?
@L Spice: It's rigorous. You find a subsequence in which the packing of the first $k$ rectangles converges to a fixed configuration. This fixed configuration (the one to which the first $k$ rectangles converges) is the one that doesn't change position when you take a subsubsequence of this subsequence. 
Dec 3 
awarded  Yearling 
Jun 1 
awarded  Nice Answer 
May 8 
awarded  Notable Question 
May 8 
revised 
Defining a canonical ordering of matrix rows/columns
added 178 characters in body 
Apr 6 
comment 
What areas of pure mathematics research are best for a postPhD transition to industry?
What do you mean coding theory is not pure math? Coding theory spans a spectrum from extremely pure math to extremely applied. Of course, you do run into the problem that pure coding theory is somewhat different from applied, but if you can find an advisor in the math department who does coding theory, I think this would be an excellent area. 
Jan 6 
awarded  Enlightened 
Jan 6 
awarded  Nice Answer 
Dec 3 
awarded  Yearling 
Sep 30 
awarded  Caucus 
Sep 18 
comment 
point in polytope
It needn't actually double the number of constraints; you can replace the inequality $\lambda_i \geq 0$ by $\lambda_i  x \geq 0$, to get the same number of constraints and one more variable. I expect you'll still take a performance hit, but less of one. 
Sep 17 
awarded  Enlightened 
Sep 17 
awarded  Nice Answer 
Sep 17 
answered  point in polytope 
Sep 13 
revised 
Algorithm on winning strategy of Winner (Simplified card game)
fixed latex and grammar 
Aug 18 
comment 
Constructing Steiner Triple Systems Algorithmically
Your nice answer makes me glad I bumped it (I fixed a broken link). 