Re: kung fu mereotopology

On Dec 22, 6:54 pm, galathaea <galath...@xxxxxxxxx> wrote:
On Dec 21, 7:44 pm, Mariano Suárez-Alvarez

<mariano.suarezalva...@xxxxxxxxx> wrote:
On Dec 22, 1:01 am, galathaea <galath...@xxxxxxxxx> wrote:
i find that kontsevich is still working on his own much
  and has a number of "huge" possibilities lurking

much of his stuff on operads
  and graph theory
  and combinatorial topology
is building some very powerful algebraic tools
which could potentially crack p = np among other big questions

Can you point to a sentence of Kontsevich related to
P = NP?

sure
  but i wasn't claiming his actually mentioning such

i was thinking of
  the algebraic approach to computational complexity

things likehttp://www.math.ntu.edu.tw/talkdata/194/March10.ppt

and from the development of operad theory
i've seen much of that computational theory
  transform to the algebraic language

particularly the theory of props in rewriting theory
  has quite some start in such a formalisation

http://sigfpe.blogspot.com/2008/10/operads-and-their-monads.html

http://blog.mikael.johanssons.org/archive/2008/02/props-and-patches/

http://www.atlantis-press.com/php/download_paper.php?id=370

and particularly
  the homological theory in computational complexity

kontsevich has been skirting algorithmic complexity
  for some time now with his work on algebraic structures
  over graphs and related combinatorial structures

probably the most suspicious to me is his
(loosely)

H (lie algebra) = H (graph complex) = H (group)
 *                 *                   *

because the homology of graph complexes
  has some immediate consequences
  for graph isomorphism and the complexity of such algorithms

i have strong suspicions
  that much of the operad theory on which this is built
  (cf.http://arxiv.org/pdf/math/0211464)
contains the kernel of the algebraic concepts
that could crack complexity questions like p =?= np

additionally
  there is known complexity work
  on poset homology
that ties their algebraics to more classical work on matroidshttp://www.springerlink.com/content/y60n827057m374n8/

kontsevich has contributed quite a bit to matroid theory
and generally has been working in that netherworld
  of the algebraics of discrete combinatorial structures
  with all the complexity issues just over the horizon


anyway
  my point was that kontsevich has done some major work
  and there is the potential
    for resolving some very big questions

Well. Duh! Do you also see potential in, say, Serre's work?


Anyways... you are able to write with so little
concreteness that it is impossible to tell whether
you actually know anything about what you write
or are simply a apt google user. You remind me distinctly
of ELIZA.

-- m

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