A quadratic lower bound for the permanent and determinant problem over any characteristic ≠ 2
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The status of the P versus NP problem
Communications of the ACM - The Status of the P versus NP Problem
Cracks in the defenses: scouting out approaches on circuit lower bounds
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Journal of Symbolic Computation
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
On P vs. NP and geometric complexity theory: Dedicated to Sri Ramakrishna
Journal of the ACM (JACM)
Geometric complexity theory and tensor rank
Proceedings of the forty-third annual ACM symposium on Theory of computing
A geometric approach to quantum circuit lower bounds
Quantum Information & Computation
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
Affine projections of polynomials: extended abstract
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the geometry of tensor network states
Quantum Information & Computation
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
The Graph Isomorphism Problem and approximate categories
Journal of Symbolic Computation
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We suggest an approach based on geometric invariant theory to the fundamental lower bound problems in complexity theory concerning formula and circuit size. Specifically, we introduce the notion of a partially stable point in a reductive-group representation, which generalizes the notion of stability in geometric invariant theory due to Mumford [Geometric Invariant Theory, Springer-Verlag, Berlin, 1965]. Then we reduce fundamental lower bound problems in complexity theory to problems concerning infinitesimal neighborhoods of the orbits of partially stable points. We also suggest an approach to tackle the latter class of problems via construction of explicit obstructions.