Efficient checking of polynomials and proofs and the hardness of approximation problems

the long version

This work is a fascinating piece of research in computer science: it is built on and combines deep theoretical results from various areas and, at the same time, takes into account applications to hard problems in several fields. The author provides important new foundational insights and essentially advances applicable techniques in such different areas as computational complexity, efficient (randomized) checking of proofs, programs and polynomials, approximation algorithms, NP-complete optimization, and error-detection and error-correction algorithms in coding theory.