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来自代表性不足群体的研究生、职业生涯早期和/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日在法国马赛伦孔特雷数学中心(CIRM)举行的关于解析函数空间内插的国际会议。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们，包括采样理论、唯一性问题和再生核Hilbert空间。国际知名数学家将进行大约20场一小时的演讲，其中许多人来自美国，他们的兴趣与插值法和解析函数空间有关。问题会议和额外的演讲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，为青年数学家和知名研究人员之间的互动提供机会是极其重要的。这些互动将通过将成为时间表一部分的休息和讨论会话来促进。在希尔伯特情形中，内插、唯一性和采样转化为再现核的几何属性。在正交化序列之后，这种核的Riesz序列(与内插有关)代表了人们在Hilbert空间中所能期望的次好的族。Riesz序列及其完全对应的Riesz基不仅有助于更好地理解潜在的Hilbert空间，而且在算子理论及其应用中发挥着核心作用，例如信号处理、数学物理和机器学习。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，在过去的十年中，当几个长期未解决的公开问题(例如，Kadison-Singer猜想和双正交指数的完备性问题)被解决时，取得了惊人的进展。会议的网站是：https://conferences.cirm-math.fr/2055.htmlThis奖反映了国家科学基金会的法定使命，通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。