I will present the paper "Learning Juntas" by Mossel, O'Donnell, and Servedio. In it, the authors give an algorithm for learning juntas (functions that depend on only k out of n relevant variables) from uniform random examples in time roughly n^(k*(??1)) where ?< 2.376 is the best known matrix multiplication exponent. This is the only improvement known over the naive algorithm which takes time roughly n^k.
The crucial arguments in the paper utilize only elementary properties of Fourier analysis of Boolean functions. Those who attended the first week or two of the mini-course should have sufficient background to follow (hopefully!).