The Usage of the Spectral Norm in Learning Theory: Some Selected Topics (invited lecture for ALT 2006) Author: Hans Ulrich Simon Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, Germany Abstract. In the talk, we review some known results about the statistical query complexity of a concept class and the spectral norm of its correlation matrix. Since spectral norms are widely used in various other areas, we are then able to put statistical query complexity in a broader context. We briefly describe some surprising connections to (seemingly) different topics in learning theory, complexity theory, and cryptography. A connection to the so-called Hidden Number Problem, which plays an important role for proving bit-security of cryptographic functions, will be discussed in somewhat more detail. ©Copyright 2006 Author