2018 John Barrett Memorial Lectures

2018年约翰·巴雷特纪念讲座

• 批准号: 1812058
• 负责人: Theodora Bourni
• 金额: $ 2.5万
• 依托单位: University of Tennessee Knoxville
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-04-01 至 2019-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1812058&HistoricalAwards=false
• 关键词: 2018; John; Barrett; Memorial; Lectures

The 2018 Barrett Lectures will take place during May 29-June 1, 2018 at the University of Tennessee, Knoxville. This year's Lectures will take the format of a workshop on recent developments in mean curvature flow, a mathematical model for the deformation of surfaces (and higher-dimensional objects) that decreases area most rapidly. The workshop is aimed at graduate students and early career researchers, as well as researchers from related applied fields in which processes like the mean curvature flow naturally arise. The workshop will consist of a one-day introductory course on mean curvature flow, followed by a series of longer form survey lectures from a selection of preeminent researchers which will introduce participants to some of the most important recent breakthroughs in the field. These lecture series will be supported by auxiliary talks from further leading researchers and a series of short talks by graduate students and early career researchers.Geometric flows, such as the mean curvature flow, have proved to be a powerful tool in the analysis of a large number of important problems in differential geometry, image processing and mathematical physics, leading to a profound impact on each of these fields. They also arise naturally in such diverse physical contexts as thermomechanics, annealing metals, crystal growth, flame propagation, wearing processes and conformal field theory, where they model physical processes involving interfaces and surface energies. The mean curvature flow is the prototypical geometric flow equation and, as such, tools developed to understand its behavior often lead to insights into the behavior of other flow-based models. The main themes to be explored at the workshop will be the uniqueness, rigidity and genericity of cylindrical singularities, the classification of ancient and soliton solutions, and recently developed entropy and noncollapsing methods.Conference website: http://www.math.utk.edu/barrett/This 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.

2018 年巴雷特讲座将于 2018 年 5 月 29 日至 6 月 1 日在诺克斯维尔田纳西大学举行。今年的讲座将采用研讨会的形式，介绍平均曲率流的最新发展，平均曲率流是一种面积减小最快的表面（和高维物体）变形的数学模型。 该研讨会面向研究生和早期职业研究人员，以及来自相关应用领域的研究人员，其中平均曲率流等过程自然出现。该研讨会将包括为期一天的平均曲率流入门课程，随后是由精选的杰出研究人员进行的一系列较长形式的调查讲座，这些讲座将向参与者介绍该领域的一些最重要的最新突破。这些讲座系列将得到进一步领先研究人员的辅助演讲以及研究生和早期职业研究人员的一系列简短演讲的支持。几何流，例如平均曲率流，已被证明是分析大型流体的强大工具。微分几何、图像处理和数学物理中的许多重要问题，对这些领域产生了深远的影响。它们还自然地出现在热力学、金属退火、晶体生长、火焰传播、磨损过程和共形场理论等不同的物理背景中，它们模拟涉及界面和表面能的物理过程。平均曲率流是典型的几何流方程，因此，为理解其行为而开发的工具通常可以深入了解其他基于流的模型的行为。研讨会将探讨的主题是圆柱奇点的独特性、刚性和通用性、古代解和孤子解的分类，以及最近开发的熵和非塌陷方法。会议网站：http://www.math.utk。 edu/barrett/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。