International Conference on Interpolation in Spaces of Analytic Functions at CIRM

CIRM 解析函数空间插值国际会议

• 批准号: 1936503
• 负责人: Brett Wick
• 金额: $ 1.2万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2020-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1936503&HistoricalAwards=false
• 关键词: International; Conference; Interpolation; Spaces; Analytic

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.

该项目的主要目标是为研究生、早期职业生涯和/或来自代表性不足群体的数学家提供参与支持，使他们能够参加在数学研究中心 (CIRM) 举行的解析函数空间插值国际会议2019 年 11 月 18 日至 22 日这一周，法国马赛​​。为期 5 天的会议将聚集对全纯插值及相关主题感兴趣的人们，包括采样理论、唯一性问题和再现核希尔伯特空间。著名国际数学家将进行大约 20 个一小时的演讲，其中许多人来自美国，对插值和解析函数空间感兴趣。 问题会议和其他有贡献的演讲也将成为会议日程的一部分。 会议组织者致力于支持妇女、少数族裔和研究人员的参与。为了促进他们作为研究人员和教育工作者的发展，为年轻数学家和知名研究人员之间的互动提供机会极其重要。 这些互动将通过休息和讨论会议来促进，这将是日程安排的一部分。在希尔伯特情况下，插值、唯一性和采样转化为复制内核的几何属性。在正交序列之后，此类核的 Riesz 序列（与插值相关）代表了希尔伯特空间中第二好的系列。 Riesz 序列及其完整对应物 Riesz 基是基本元素，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（例如信号处理、数学物理和机器学习）中发挥着核心作用。我们对 Riesz 基在控制理论中的使用特别感兴趣。我们还注意到，在过去十年中，解决了几个长期存在的开放问题（例如，卡迪森-辛格猜想和双正交指数的完整性问题），取得了惊人的进展。会议网站可访问：https://conferences.cirm-math.fr/2055.html 该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。