International Conference on Interpolation in Spaces of Analytic Functions at CIRM

Washington University, Saint Louis MO

Investigators

Abstract

The primary goal of this project is to provide participant support for graduate students, early-career, and/or mathematicians from underrepresented groups allowing them to attend the international conference on Interpolation in Spaces of Analytic Functions at the Centre de Rencontres Mathematiques (CIRM) in Marseille, France during the week of November 18-22, 2019. The 5-day conference will gather people interested in holomorphic interpolation and related subjects, including sampling theory, uniqueness problems, and reproducing kernel Hilbert spaces. There will be approximately 20 one-hour talks by prominent international mathematicians, many of them from the U. S., with interests related to interpolation and spaces of analytic functions. A problem session and additional contributed talks will also be part of the conference schedule. The organizers of the conference are committed to supporting the participation of women, minorities, and researchers. To facilitate their development as researchers and educators, it is extremely important to provide opportunities for the interaction between young mathematicians and established researchers. These interactions will be facilitated by the breaks and discussion sessions that will be part of the schedule. In the Hilbertian situation, interpolation, uniqueness, and sampling translate to geometric properties of reproducing kernels. After orthonormal sequences, Riesz sequences of such kernels (which are related to interpolation) represent the second-best family one can expect in a Hilbert space. Riesz sequences, and their complete counterpart, Riesz bases, are fundamental elements contributing not only to a better understanding of the underlying Hilbert spaces, but playing a central role in operator theory and its applications, such as signal processing, mathematical physics, and machine learning. We are particularly interested in the use of Riesz bases in control theory. We also note that in the last decade spectacular progress was made when several longstanding open problems were solved (e.g., the Kadison-Singer conjecture and the completeness problem for biorthogonal exponentials). The conference website can be found at: https://conferences.cirm-math.fr/2055.html This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.