P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Lower Bounds in a Parallel Model without Bit Operations
SIAM Journal on Computing
Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems
SIAM Journal on Computing
A polynomiality property for Littlewood-Richardson coefficients
Journal of Combinatorial Theory Series A
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Proving SAT does not have small circuits with an application to the two queries problem
Journal of Computer and System Sciences
Geometric Complexity Theory II: Towards Explicit Obstructions for Embeddings among Class Varieties
SIAM Journal on Computing
Algebrization: A New Barrier in Complexity Theory
ACM Transactions on Computation Theory (TOCT)
Proving lower bounds via pseudo-random generators
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
On the complexity of mixed discriminants and related problems
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
The GCT program toward the P vs. NP problem
Communications of the ACM
Geometric complexity theory III: on deciding nonvanishing of a Littlewood---Richardson coefficient
Journal of Algebraic Combinatorics: An International Journal
Explicit lower bounds via geometric complexity theory
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Non-commutative arithmetic circuits with division
Proceedings of the 5th conference on Innovations in theoretical computer science
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This article gives an overview of the geometric complexity theory (GCT) approach towards the P vs. NP and related problems focusing on its main complexity theoretic results. These are: (1) two concrete lower bounds, which are currently the best known lower bounds in the context of the P vs. NC and permanent vs. determinant problems, (2) the Flip Theorem, which formalizes the self-referential paradox in the P vs. NP problem, and (3) the Decomposition Theorem, which decomposes the arithmetic P vs. NP and permanent vs. determinant problems into subproblems without self-referential difficulty, consisting of positivity hypotheses in algebraic geometry and representation theory and easier hardness hypotheses.