Geometric Analysis Conferences and Seminars

几何分析会议和研讨会

• 批准号: 1611717
• 负责人: Paul Feehan
• 金额: $ 3万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1611717&HistoricalAwards=false
• 关键词: Geometric; Analysis; Conferences; Seminars

This award supports a series of three two-day Geometric Analysis conferences at Rutgers University, on October 27-28 in 2016, October 26-27 in 2017, and October 25-26 in 2018, that highlight recent developments in the analysis of non-linear elliptic and parabolic partial differential equations arising in the study of Riemannian manifolds and geometric flows. Riemannian manifolds are higher-dimensional generalizations of the familiar concept of a surface in three-dimensional space, such as the surface of a ball or a donut. Four-dimensional manifolds (with three spatial and one temporal direction) are used in general relativity as models for the universe. Manifolds of other dimensions are used by theoretical physicists in string theory, which may lead to a unification of quantum field theory and gravity. The conferences will bring together distinguished senior speakers and a wide range of junior mathematicians to disseminate recent research progress and catalyze future research in the subject. The opportunities presented by the meetings to discuss research with leaders in the field will help to train and encourage the next generation of researchers. The conference series makes special efforts to encourage women and minority mathematicians to participate in the meetings. The field of geometric flows is of great current interest due its many applications to the understanding of Riemannian manifolds. Within Ricci flow for a Riemannian metric, there has been progress in understanding the structure of solutions, their singularities, their asymptotics, and uniqueness. Flows starting from more general initial data (for example, a metric space, or a manifold with unbounded curvature, or an incomplete metric) are becoming better understood. A better understanding of Ricci flow may lead to advances in areas such as general relativity, string theory, the geometry of closed four-dimensional smooth manifolds, and renormalization in quantum field theory. The study of mean curvature flow may lead to advances in knot theory, image processing, materials science, and minimal surfaces. The conference series brings together experts at the frontier of research in these various topics from around the United States. The conference is expected to generate transfers of knowledge, new collaborations, and a cross-fertilization of ideas, and further inspire graduate students and junior mathematicians. The 2016 conference website is www.finmath.rutgers.edu/ga2016/index.php

该奖项支持在罗格斯大学举行的一系列为期两天的几何分析会议，分别于2016年10月27日至28日，2017年10月26日至27日和2018年10月25日至26日举行，突出了黎曼流形和几何流研究中产生的非线性椭圆和抛物偏微分方程分析的最新进展。黎曼流形是三维空间中熟悉的曲面概念的高维推广，例如球或甜甜圈的曲面。四维流形（具有三个空间方向和一个时间方向）在广义相对论中被用作宇宙的模型。理论物理学家在弦理论中使用了其他维度的流形，这可能会导致量子场论和引力的统一。会议将汇集杰出的高级发言人和广泛的初级数学家，传播最新的研究进展，并促进该主题的未来研究。 会议提供的与该领域领导人讨论研究的机会将有助于培训和鼓励下一代研究人员。会议系列作出特别努力，鼓励妇女和少数民族数学家参加会议。几何流的领域是目前极大的兴趣，由于其许多应用程序的理解黎曼流形。在黎曼度量的里奇流中，在理解解的结构、奇性、渐近性和唯一性方面取得了进展。从更一般的初始数据（例如，度量空间，或具有无界曲率的流形，或不完全度量）开始的流正变得更好理解。更好地理解里奇流可能会导致在广义相对论、弦理论、封闭四维光滑流形的几何学和量子场论中的重整化等领域的进步。平均曲率流的研究可能会导致纽结理论，图像处理，材料科学和极小曲面的进步。该系列会议汇集了来自美国各地的这些不同主题研究前沿的专家。会议预计将产生知识的转移，新的合作，和思想的交叉施肥，并进一步激励研究生和初级数学家。2016年会议网址为www.finmath.rutgers.edu/ga2016/index.php