Conference on Analysis, Dynamics, Geometry, and Probability

分析、动力学、几何和概率会议

• 批准号: 1954590
• 负责人: Raanan Schul
• 金额: $ 3万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-02-01 至 2021-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1954590&HistoricalAwards=false
• 关键词: Conference; Analysis; Dynamics; Geometry; Probability

This award supports participation in the workshop "Analysis, Dynamics, Geometry, and Probability" held at the Simons Center for Geometry and Physics (SCGP, located in Stony Brook, NY) on March 2-6, 2020. Although the central questions studied in these fields are different, they have had fruitful interaction, and each field has benefited from developments in the others. While some of these connections are centuries old, there have been exciting developments in recent years. The award will allow a diverse group of mostly early-career mathematicians to interact with more established researchers. Bringing together this group will provide an excellent opportunity for interaction, shared insight, and further development. The organizers expect this to be a valuable educational opportunity as well as a research conference. Holding this conference at the SCGP will make it accessible and visible to the physics community, leading to interactions that might not occur as readily otherwise.The workshop will bring together experts from interconnected fields. One example is the connection between Brownian motion, harmonic measure, analysis of singular integrals, and geometric properties of domains. This topic relates how a randomly-moving particle sees the boundary of the region in which it moves, the equilibrium charge distribution on the boundary of this region, and classical questions in analysis. Another example concerns function theory and dynamical systems: which geometric properties of functions are most important in studying the associated dynamical system formed by the iterates of the function, and on the other hand, what can the dynamical system tell us about the geometry of the initial function? The speakers include prominent researchers from a wide range of areas, including computer science, applied mathematics, dynamical systems, probability, analysis, and geometry. Many speakers have a history of making good use of such interchanges for groundbreaking work, some with important practical applications. Some specific examples are Ingrid Daubechies’ work on wavelets and their numerous applications (for example, image compression), Peter Jones’ work on diffusion geometry for data analysis, Svitlana Mayboroda’s work on localization of waves (used in LED light design), and Assaf Naor’s work on metric embeddings and algorithms, with applications in computer science. For more details see http://scgp.stonybrook.edu/archives/29488This 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.

该奖项支持参加2020年3月2日至6日在西蒙斯几何与物理中心（SCGP，位于纽约州斯托尼布鲁克）举行的“分析，动力学，几何和概率”研讨会。虽然这些领域研究的中心问题不同，但它们有着富有成效的互动，每个领域都从其他领域的发展中受益。虽然其中一些联系已经有几个世纪的历史，但近年来出现了令人兴奋的发展。该奖项将允许一个多元化的群体，主要是早期职业数学家与更成熟的研究人员互动。将这一群体聚集在一起将为互动、分享见解和进一步发展提供一个极好的机会。组织者希望这是一个宝贵的教育机会，以及一个研究会议。在SCGP举办这次会议将使物理学界能够接触到并看到它，从而导致可能不会轻易发生的互动。研讨会将汇集来自相互关联领域的专家。一个例子是布朗运动，调和测度，奇异积分分析和域的几何性质之间的联系。本主题涉及随机运动的粒子如何看待其运动区域的边界、该区域边界上的平衡电荷分布以及分析中的经典问题。另一个例子涉及函数论和动力系统：函数的哪些几何性质在研究由函数的迭代形成的相关动力系统时最重要，另一方面，动力系统能告诉我们关于初始函数的几何的什么？演讲者包括来自广泛领域的杰出研究人员，包括计算机科学，应用数学，动力系统，概率，分析和几何。许多发言者都有很好地利用这种交流进行开创性工作的历史，其中一些具有重要的实际应用。一些具体的例子是Ingrid Daubechies在小波及其众多应用（例如，图像压缩）方面的工作，Peter Jones在数据分析中的扩散几何方面的工作，Svitlana Mayboroda在波的局部化方面的工作（用于LED灯设计），以及Assaf Naor在度量嵌入和算法方面的工作，以及计算机科学中的应用。欲了解更多详细信息，请参阅http://scgp.stonybrook.edu/archives/29488This奖项反映了NSF的法定使命，并已被认为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。