Conference on Geometric Analysis

该奖项旨在支持参加几何分析国际合作研究小组会议的美国参与者，该会议将于2017年7月24日至7月28日在加拿大不列颠哥伦比亚大学太平洋数学科学研究所(PIMS)举行。一般而言，几何分析涉及使用解析方法来解决微分几何和广义相对论中的问题。该讲习班将汇集数学家，包括该领域的顶尖专家，以交流最新进展，并促进参与者之间的互动和合作。特别是，会议的目标是传播几何分析的新进展，为研究生的培养做出贡献，并将一大批数学家带到交流和孵化新的数学思想。为了实现这些目标，特别鼓励初级研究人员(包括博士后研究员和研究生)和来自不同代表性不足群体的研究人员申请，并将优先获得组委会的资金支持。研讨会将邀请来自世界各地的顶尖专家介绍几何分析的新结果和/或当前进展的综述，特别是从以下子领域：(1)包括曲率流的几何PDE分析(例如，高斯曲率流、Ricci流、梯度Ricci孤子和具有较低Ricci曲率界的流形的幂)；(2)Kahler-Einstein度量和Kahler-Ricci流(例如，奇异Kahler度量，Kahler流形的Gromov-Hausdorff极限，Kahler-Ricci流的正则性和弱解，以及Kahler-Ricci孤子)；(3)极小子流形和平均曲率流(例如，镜像对称中的特殊拉格朗日子流形，Willmore猜想证明的极小-极大理论，以及平均曲率流奇点的形成)；以及(4)数学广义相对论(例如，具有常平均曲率的类空超曲面、质量中心和非线性胶合方法)。自2010年PIMS几何分析研讨会以来，这些领域出现了许多令人振奋的新成果和新技术，会议将有大约25名演讲者讨论这些进展。研讨会的演讲摘要和视频将张贴在会议网页http://www.pims.math.ca/scientific-event/170724-ccga上

This award is to support U.S. participants in the International Collaborative Research Group Conference on Geometric Analysis, to be held at the Pacific Institute for the Mathematical Sciences (PIMS), University of British Columbia, Canada from July 24 to July 28, 2017. Generally speaking, geometric analysis involves using analytic methods to solve problems in differential geometry and general relativity. This workshop will bring together mathematicians, including top experts in the field, to communicate recent progress and to promote interaction and collaboration among the participants. In particular, the goals of the conference are to disseminate new advances in geometric analysis, to contribute to the training of graduate students, and to bring a large group of mathematicians to exchange and to incubate new mathematical ideas. To realize these goals, junior researchers (including postdoctoral fellows and graduate students) and researchers from various under-represented groups are especially encouraged to apply and will be given priority for financial support from the organizing committee.The workshop will bring leading experts from all over the world to present the new results and/or surveys of current progresses in geometric analysis, in particular, from the following subfields: (1) Analysis of geometric PDE including curvature flows (e.g., power of Gauss curvature flow, Ricci flow, gradient Ricci solitons, and manifolds with lower Ricci curvature bound); (2) Kahler-Einstein metrics and the Kahler-Ricci flow (e.g., singular Kahler metrics, the Gromov-Hausdorff limits of Kahler manifolds, the regularity and weak solutions of Kahler-Ricci flow, and Kahler-Ricci solitons); (3) Minimal submanifolds and mean curvature flow (e.g., special Lagrangian submanifolds in mirror symmetry, min-max theory from the proof of Willmore conjecture, and the formation of singularities of mean curvature flow); and (4) Mathematical general relativity (e.g., space-like hypersurfaces with constant mean curvature, the center of mass, and the nonlinear gluing approach). Since 2010 PIMS Workshop on Geometric Analysis, there are many exciting new results and new techniques in these fields, and the conference will have about 25 speakers discussing these advances. The abstract of talks and videos from the workshop will be posted on the conference webpage http://www.pims.math.ca/scientific-event/170724-ccga