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

该奖项支持罗格斯大学举行的一系列为期两天的三场几何分析会议，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，这些会议强调了非几何分析的最新进展。在黎曼流形和几何流研究中出现的线性椭圆和抛物型偏微分方程。黎曼流形是三维空间中熟悉的表面概念（例如球或甜甜圈的表面）的高维推广。四维流形（具有三个空间方向和一个时间方向）在广义相对论中用作宇宙模型。理论物理学家在弦理论中使用其他维度的流形，这可能会导致量子场论和引力的统一。这些会议将汇集杰出的资深演讲者和广泛的初级数学家，以传播最新的研究进展并促进该学科的未来研究。 会议提供了与该领域的领导者讨论研究的机会，将有助于培训和鼓励下一代研究人员。该系列会议特别努力鼓励女性和少数族裔数学家参加会议。几何流领域目前备受关注，因为它在理解黎曼流形方面有许多应用。在黎曼度量的 Ricci 流中，在理解解的结构、奇点、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，或不完整度量）开始的流正在变得更好地理解。对利玛窦流的更好理解可能会带来广义相对论、弦理论、封闭四维光滑流形几何以及量子场论重整化等领域的进步。平均曲率流的研究可能会促进结理论、图像处理、材料科学和最小曲面的进步。该会议系列汇集了来自美国各地这些不同主题的前沿研究专家。此次会议预计将产生知识转移、新的合作和思想的交叉传播，并进一步激励研究生和初级数学家。 2016年会议网站是www.finmath.rutgers.edu/ga2016/index.php