Conference on Analysis, Dynamics, Geometry, and Probability

该奖项支持参加2020年3月2-6日在纽约州石溪的西蒙斯几何和物理中心(SCGP)举办的“分析、动力学、几何和概率”研讨会。尽管这些领域研究的中心问题不同，但它们进行了卓有成效的互动，每个领域都从其他领域的发展中受益。虽然其中一些联系有几百年的历史，但近年来出现了令人兴奋的发展。该奖项将允许一个主要由职业生涯早期的数学家组成的多样化群体与更成熟的研究人员互动。将这一群体聚集在一起将提供一个互动、分享见解和进一步发展的绝佳机会。组织者希望这既是一次宝贵的教育机会，也是一次研究会议。在SCGP举行这次会议将使物理界能够接触到和看到它，导致可能不会轻易发生的相互作用。研讨会将汇集来自相互关联的领域的专家。一个例子是布朗运动、调和测度、奇异积分分析和区域的几何性质之间的联系。这个主题涉及随机运动的粒子如何看到它运动的区域的边界，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：在研究由函数的迭代形成的相关动力系统时，函数的哪些几何性质是最重要的，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知名研究人员，包括计算机科学、应用数学、动力系统、概率、分析和几何。许多演讲者有很好地利用这种立交桥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关于小波及其众多应用的工作(例如，图像压缩)、Peter Jones关于用于数据分析的扩散几何的工作、Svitlana Mayboroda关于波的局部化的工作(用于LED灯设计)以及Assaf Naor关于公制嵌入和算法的工作以及在计算机科学中的应用。有关更多细节，请参阅http://scgp.stonybrook.edu/archives/29488This奖项，该奖项反映了美国国家科学基金会的法定使命，并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。

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.