4,573 reputation
2855
bio website math.mit.edu/~shor
location M.I.T., Cambridge, MA
age 55
visits member for 5 years
seen Dec 13 at 19:43

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.


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).
Aug
18
awarded  Excavator
Aug
18
revised Constructing Steiner Triple Systems Algorithmically
fixed broken link
Jul
2
comment Largest graphs of girth at least 6
@Brendan: the reason I came upon this question was looking at sequence A072567 in the Online Encyclopedia of Integer Sequences. The $m$th term is the number of edges in the largest bipartite subgraph of $K_{m,m}$ (which is tangentially related to a quantum game I'm looking at). So after you've checked this table, if all your bipartite graphs for even $n$ are split $n/2,n/2$, you could easily extend this sequence.
Jul
2
comment Largest graphs of girth at least 6
Some numerology: 15, 27, and 43 are one more than 14, 26 and 42, respectively. For these numbers, the unique optimum bipartite graph of girth 6 is based on the point-line incidence structure of a projective plane with $n= 2(q^2+q+1)$ and $e = (q+1) (q^2+q+1)$.