Dedicated to Sri Ramakrishna
- Lower Bounds in a Parallel Model without bit operations, SIAM J. Comput., 28, (1999), pp. 1460-1509.
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Geometric Complexity Theory: Abstract,
Technical Report TR-2007-12, computer science
department, The University of Chicago, September, 2007.
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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.
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(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.
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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.
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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.
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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.
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Erratum to the saturation hypothesis in "Geometric Complexity Theory VI",
Technical Report TR-2008-10, computer science
department, The University of Chicago, October, 2008.