Dedicated to Sri Ramakrishna

• Lower Bounds in a Parallel Model without bit operations, SIAM J. Comput., 28, (1999), pp. 1460-1509.
  
• Geometric Complexity Theory: Abstract, Technical Report TR-2007-12, computer science department, The University of Chicago, September, 2007.
• 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.
• (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.
• (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. cs.ArXiv preprint cs.CC/0612134, December 25, 2006. To appear in SIAM J. Comput.
• (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 saturated and positive integer programming in representation theory and algebraic geometry, Technical Report TR-2007-04, computer science department, The University of Chicago, May, 2007.
• 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.
• Erratum to the saturation hypothesis in "Geometric Complexity Theory VI", Technical Report TR-2008-10, computer science department, The University of Chicago, October, 2008.