Computational Complexity

computational complexity presents outstanding research in computational complexity. Its subject is at the interface between mathematics and theoretical computer science, with a clear mathematical profile and strictly mathematical format.

The central topics are:

Models of computation, complexity bounds (with particular emphasis on lower bounds), complexity classes, trade-off results

for sequential and parallel computation

for "general" (Boolean) and "structured" computation (e.g. decision trees, arithmetic circuits)

for deterministic, probabilistic, and nondeterministic computation

worst case and average case

Specific areas of concentration include:

Structure of complexity classes (reductions, relativization questions, degrees, derandomization)

Algebraic complexity (bilinear complexity, computations for polynomials, groups, algebras, and representations)

Interactive proofs, pseudorandom generation, and randomness extraction

Complexity issues in:

crytography

learning theory

number theory

logic (complexity of logical theories, cost of decision procedures)

combinatorial optimization and approximate Solutions

distributed computing

property testing.