Dedicated to Sri Ramakrishna


An Overview of GCT
  • On P vs. NP, and Geometric Complexity Theory, JACM, vol. 58, issue 2, April 2011.
  • FOCS 2010 Tutorial based on this overview.
    The defining Flip strategy of GCT
  • Explicit Proofs and The Flip, Technical Report, Computer Science Department, The University of Chicago, September 2010.
    GCT Papers
  • Lower Bounds in a Parallel Model without bit operations, SIAM J. Comput., 28, (1999), pp. 1460-1509.
  • (With M. Sohoni) Geometric complexity theory I: An approach to the P vs. NP and related problems, SIAM J. Comput., vol 31, no. 2, pp. 496-526, (2001).
  • (With M. Sohoni) Geometric complexity theory II: Towards explicit obstructions for embeddings among class varieties. SIAM J. Comput., Vol. 38, Issue 3, June 2008.
  • (With M. Sohoni) Geometric complexity theory, P vs. NP and explicit obstructions, in "Advances in Algebra and Geometry", Edited by C. Musili, the proceedings of the International Conference on Algebra and Geometry, Hyderabad, 2001.
  • (With M. Sohoni) Geometric complexity theory III: on deciding positivity of Littlewood-Richardson coefficients, cs.ArXiv preprint cs.CC/0501076 v1 26 Jan 2005
  • (With M. Sohoni) Geometric complexity theory IV: quantum group for the Kronecker problem, preprint, computer science department, The University of Chicago, March, 2007.
  • (With Hariharan Narayanan) Geometric Complexity Theory V: On deciding nonvanishing of a generalized Littlewood-Richardson coefficient, Technical Report TR-2007-05, computer science department, The University of Chicago, May, 2007.
  • Geometric Complexity Theory VI: the flip via positivity, Technical Report, computer science department, The University of Chicago, January 2011.
  • Geometric Complexity Theory VII: Nonstandard quantum group for the plethysm problem, Technical Report TR-2007-14, computer science department, The University of Chicago, September, 2007.
  • Geometric Complexity Theory VIII: On canonical bases for the nonstandard quantum groups, Technical Report TR-2007-15, computer science department, The University of Chicago, September, 2007.
    Lecture notes on GCT
  • On P vs. NP, Geometric Complexity Theory, and the Riemann Hypothesis, Technical Report, Computer Science department, The University of Chicago, August, 2009. cs.ArXiv preprint cs.CC/0908.1936
    This overview is based on a series of three lectures. Video lectures in this series are available here.
  • (With M. Sohoni) Geometric Complexity Theory: Introduction, Technical Report TR-2007-16, computer science department, The University of Chicago, September, 2007. Lecture notes for an introductory graduate course on geometric complexity theory in the computer science department, the university of Chicago.
  • On P vs. NP, Geometric Complexity Theory, and The Flip I: a high-level view, Technical Report TR-2007-13, computer science department, The University of Chicago, September, 2007.