Recently the learning problems took the center stage in area of theoretical computer science. An amazing and beautiful thing is that they are harmonic analysis problems at heart. The lecture concerns with some natural and elementary question of learning theory and the approach to learning via harmonic analysis. Suppose you wish to find a N by N matrix by asking this matrix question that it honestly answers. For example you can ask question ``What is your (1,1) element?'' Obviously you will need $N^2$ many questions like that. But if one knows some information on Fourier side one can ask only log log N questions if they are carefully randomly chosen. Of course one pays the price: first of all one would find the matrix only with high confidence (high probability bigger than $1-\delta$), secondly with the error $\epsilon$. Such learning is known as PAC learning, PAC stands for `probably approximately correct'. The origins of the problem are in theoretical computer science, but the methods are pure harmonic analysis and probability. The main ingredient is dimension free Bernstein—Remez inequality.
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006