Polona Durcik,
Irina Holmes Fay,
and Paata Ivanisvili

Original Announcement

This workshop will be devoted to
analysis on the hypercube. The set of vertices of a unit cube is
called the hypercube. It consists of vectors with coordinates zeros
and ones. Series of open questions in computer science, especially in
quantum computing such as Aaronson-Ambainis conjecture, can be
formulated as mathematical problems on the hypercube which do not
require any a priori knowledge of computer science to start solving
them. It turns out that these questions have certain Fourier-analytic
nature if one considers the hypercube as a Cantor group equipped with
uniform measure. Unlike the classical case of the unit circle, many
fundamental results in classical Fourier analysis and approximation
theory, including Markov-Bernstein type inequalities, are not yet
developed well enough to solve the problems raised in computer
science. The goal of the workshop is to bring researchers with
different backgrounds, including analysis, probability, combinatorics,
and computer science, in order to introduce them to open problems on
the hypercube, give lectures on the subject, strengthen the bridges
between fields that overlap with the hypercube, and describe the
recent results in this area