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