International Conference on Interpolation in Spaces of Analytic Functions at CIRM

该项目的主要目标是为研究生，早期职业生涯和/或数学家提供参与者支持，使他们能够参加2019年11月18日至22日在法国马赛的数学中心（CIRM）举行的解析函数空间插值国际会议。为期5天的会议将聚集对全纯插值和相关主题感兴趣的人，包括采样理论，唯一性问题和再生核希尔伯特空间。届时将有大约20场由国际著名数学家主持的一小时讲座，其中许多来自美国。美国，对插值和解析函数空间感兴趣。 一个问题会议和额外的贡献会谈也将是会议日程的一部分。 会议的组织者致力于支持妇女、少数民族和研究人员的参与。为了促进他们作为研究人员和教育工作者的发展，为年轻数学家和既定研究人员之间的互动提供机会是极其重要的。 这些互动将通过时间表中的休息和讨论来促进。在希尔伯特的情况下，插值，唯一性和采样转化为再生核的几何性质。在标准正交序列之后，这种核的Riesz序列（与插值有关）代表了希尔伯特空间中第二好的家族。Riesz序列及其完全对应物Riesz基不仅有助于更好地理解底层希尔伯特空间，而且在算子理论及其应用（如信号处理，数学物理和机器学习）中发挥着核心作用。我们对Riesz基在控制理论中的应用特别感兴趣。我们还注意到，在过去十年中，当几个长期悬而未决的问题得到解决时，取得了惊人的进展（例如，Kadison-Singer猜想和双正交指数的完备性问题）。该会议的网站可以在：https://conferences.cirm-math.fr/2055.htmlThis奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。

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.htmlThis 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.