4,678 reputation
2955
bio website math.mit.edu/~shor
location M.I.T., Cambridge, MA
age 56
visits member for 5 years, 9 months
seen Aug 8 at 23:13

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.


Aug
1
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 post-PhD 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).