Harmonic analysis on boolean cube and beyond and some application to learning

Classical harmonic analysis (Poincare inequalities, singular operators) being moved to discrete setting reveals many surprises.

It also proves to be rather useful in providing the solutions to old problems of Banach space theory, graph theory and theoretical computer science.

I will present examples of the successful applications of harmonic analysis on hypercube (and beyond) to solve some problems in these areas.

The emphasis will be made on non-commutative Bohnenblust—Hille inequality, dimension free discrete Remez inequality, and their application to learning big matrices by small number of queries.

You can learn more about Professor Alexander Volberg here: https://users.math.msu.edu/users/volberg/