In this talk I am discussing polynomial approximation problems on the n-dimensional hypercube, focusing on quantitative estimates of the approximation error as n grows. This topic represents a burgeoning area in the analysis of Boolean functions—one that is far less understood than its classical counterpart on the real line. I am presenting several recent results together with its applications, as well as highlighting ongoing challenges and open problems in the field.
Here is a screenshot from one of Jean Bourgain’s papers from 2001:
Zeros and Ones 