Rutgers Geometric Analysis Conference 2022

该奖项支持参加2022年5月16日至20日在新不伦瑞克新泽西州立大学罗格斯大学学院大道校区举行的罗格斯几何分析会议。这次会议是为期五天的会议，为期一天的暑期学校包括三个迷你课程和四天的研究讲座，来自美国和欧洲的21位顶尖数学家。此次活动的科学主题包括几何分析、数学物理以及低维拓扑和辛几何的应用。参与者将与一群杰出的、多元化的数学领袖和后起之秀进行互动。这次会议的目的是促进知识的转移、新的合作和思想的交叉培养，并进一步激励研究生和职业生涯早期的数学家。几何分析、数学物理以及低维拓扑和辛几何的应用最近取得了令人兴奋的进展。例如，几何流由于其许多应用而引起了人们的极大兴趣。对于Ricci流，在理解解的结构、奇性、渐近极限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)开始的流正在变得更好地理解。对Ricci流的更好的理解可能会导致诸如广义相对论、弦理论、低维拓扑和量子场论中的重整化等领域的进展。对平均曲率流的进一步研究可能会在广义相对论、图像处理、材料科学和极小曲面方面取得进展。会议将汇集来自世界各地这些领域研究前沿的专家。会议网站是：https://www.sas.rutgers.edu/cms/finmath/geometric-analysis-conf-2022This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优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports participation in the Rutgers Geometric Analysis Conference held May 16-20, 2022, on the College Avenue Campus of Rutgers, The State University of New Jersey, New Brunswick. The conference is a five-day meeting with a one-day summer school comprising three mini-courses and four days of research talks by twenty-one leading mathematicians from the United States and Europe. The scientific themes of the event include geometric analysis, mathematical physics, and applications to low-dimensional topology and symplectic geometry. The participants will interact with a distinguished and diverse group of mathematical leaders and rising stars. The conference aims to generate transfers of knowledge, new collaborations, and a cross-fertilization of ideas, and further inspire graduate students and early-career mathematicians.There has been exciting recent progress in geometric analysis, mathematical physics, and applications to low-dimensional topology and symplectic geometry. For example, geometric flows are of great current interest due to their many applications. For Ricci flow, there has been progress in understanding the structure of solutions, their singularities, their asymptotic limits, 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. An improved understanding of Ricci flow may lead to advances in areas such as general relativity, string theory, low-dimensional topology, and renormalization in quantum field theory. Further study of mean curvature flow may lead to advances in general relativity, image processing, material science, and minimal surfaces. The meeting will bring together experts at the frontier of research in these areas from around the world.The conference website is: https://www.sas.rutgers.edu/cms/finmath/geometric-analysis-conf-2022This 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.