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Analysis on the hypercube with applications to quantum computing
7 June - 12 June
This workshop, sponsored by AIM and the NSF, 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
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.