Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

Atrium > Mathematics, Physics & Philosophy: Geometric Complexity Theory & Category Theory

Bottom of Page

1 to 6 of 6

  1.  
    • CommentRowNumber1.
    • CommentAuthortrent
    • CommentTimeMay 6th 2014
    • (edited May 6th 2014)
    Perhaps this is better suited to mathoverflow or theoretical comp sci stack exchange (so, feel free to delete this), but, does anyone know whether there is work which applies category theory to geometric complexity theory? (GCT is algebraic geometry & representation theory applied to computational complexity theory. It has been called "the string theory of computer science". If you already know basic cct, see these ias talks for an intro to gct: http://video.ias.edu/csdm/pvsnp . (I'm not knowledgeable about theoretical computer science at all...just a math major starting to dabble in cct for fun.))
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2014

    There is somebody who once wrote a brief post “Rethinking geometric complexity theory” (ask Google, I am on my phone), suggesting that monoidal category theory should help. I gather Mulmuley’s program involves quantum groups? That will be the hook into TQFT and hence monoidal category theory.

    • CommentRowNumber3.
    • CommentAuthortrent
    • CommentTimeMay 7th 2014
    Thanks, found it on a blog called "the salty schemer" (after the programming language, not the things in algebraic geometry). http://salty-schemer.blogspot.com/2011/08/rethinking-geometric-complexity-theory.html?m=1 I wonder whether the author has made any progress along those lines since 2011.
    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 7th 2014
    • (edited May 7th 2014)

    Can you isolate how much quantum groups control the program? By Tannaka duality, Quantum groups are really just a dual placeholder for their monoidal categories of representations. To the extent that GCT is about quantum groups, we’ll have the answer to your quetion.

    • CommentRowNumber5.
    • CommentAuthortrent
    • CommentTimeMay 7th 2014
    I can once I finish studying basic CCT and move on to GCT.
    • CommentRowNumber6.
    • CommentAuthortrent
    • CommentTimeSep 15th 2014

    Haven’t had time to actually explore GCT yet, but I just noticed that the Simons Institute for the Theory of Computing is dedicating this fall to Algorithms and Complexity in Algebraic Geometry and recording everything: http://simons.berkeley.edu/programs/algebraicgeometry2014. For any non - computer scientists who need a crash course in computational complexity theory before exploring GCT, Tim Gowers is your man: http://sms.cam.ac.uk/collection/545358

1 to 6 of 6

  1.