2018 John Barrett Memorial Lectures

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。今年的讲座将采取研讨会的形式，介绍平均曲率流的最新发展，平均曲率流是一种表面(和高维物体)变形的数学模型，面积减少得最快。该研讨会面向研究生和早期职业研究人员，以及来自像平均曲率流这样的过程自然产生的相关应用领域的研究人员。研讨会将包括为期一天的平均曲率流入门课程，随后将由一批杰出的研究人员举办一系列较长形式的调查讲座，向与会者介绍该领域一些最重要的最新突破。这些系列讲座将由更多顶尖研究人员的辅助演讲和研究生和早期职业研究人员的一系列简短演讲支持。几何流动，如平均曲率流，已被证明是分析微分几何、图像处理和数学物理中大量重要问题的强大工具，对这些领域都产生了深远的影响。它们也自然地出现在各种各样的物理环境中，如热力学、退火金属、晶体生长、火焰传播、磨损过程和保形场理论，在这些环境中，它们对涉及界面和表面能量的物理过程进行建模。平均曲率流是典型的几何流方程，因此，为了解其行为而开发的工具通常会导致对其他基于流的模型的行为的深入了解。研讨会的主要主题将是柱状奇点的唯一性、刚性和通用性，古代和孤子解的分类，以及最近开发的熵和非坍塌方法。会议网站：http://www.math.utk.edu/barrett/This奖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价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.