Harmonic Analysis

The field of Harmonic Analysis dates back to the 19th century, and has its roots in the study of the decomposition of functions using Fourier series and the Fourier transform.  In recent decades, the subject has undergone a rapid diversification and expansion, though the decomposition of functions and operators into simpler parts remains a central tool and theme.  

This program will bring together researchers representing the breadth of modern Harmonic Analysis and will seek to capitalize on and continue recent progress in four major directions: Restriction, Kakeya, and Geometric Incidence Problems; Analysis on Nonhomogeneous Spaces; Weighted Norm Inequalities; and Quantitative Rectifiability and Elliptic PDE.  Many of these areas draw techniques from or have applications to other fields of mathematics, such as analytic number theory, partial differential equations, combinatorics, and geometric measure theory.  

Professor Alexander Volberg (Michigan State) has been appointed as a Clay Senior Scholar from January to May 2017 to participate in this program.