Conference: Geometry and Analysis of Groups and Manifolds

该奖项为美国的早期职业数学家提供旅行支持，参加2023年6月26日至6月30日在意大利比萨举行的为期一周的会议。会议的主题是“群和流形的几何与分析”。会议涉及来自三个不同数学社区的参与者和发言者，即几何流，度量空间分析和几何群论，重点是这些领域之间的联系。我们的目标是为这些不同的数学家社区之间的合作创造一个有利的环境。美国早期职业数学家参加这样的重大会议，将有助于保持和加强美国在相关领域数学科学研究的领先地位。主要研究人员和组委会将共同努力，以确定和支持来自数学代表性不足的群体的参与者。会议将为早期职业数学家举办海报会议，展示他们的作品，并选择其中一些进行简短的谈话。本次会议还将传播知识，以更广泛的数学界作为组织者计划记录所有的谈话，并把录音在互联网上。近年来，有很强的互动问题之间的几何分析和低维拓扑/几何群论。一方面，低维拓扑学和几何群论中的问题和例子激发了几何分析的快速发展。另一方面，分析方法已被用于证明低维拓扑学和几何群论中的深定理。这些领域之间有一些新兴的新联系，例如Kleiner-Muller-Xie最近的工作，他们使用几何映射理论的分析方面的思想来研究某些空间和群之间的拟共形映射的刚性和正则性，Kleiner-Lang的工作，他们使用几何测度理论中的度量流来研究Gromov双曲空间的高阶类似物的大尺度几何，工作的宋球面高原问题的组同源性连接几何变分问题的代数和拓扑性质的群体等会议的目标是汇集专家从这些不同的领域交换意见和合作的重要问题在这些领域。更多细节可以在会议网站上找到：https://sites.google.com/view/geometryandanalysis/This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

This award provides travel support for U.S. based early career mathematicians to attend a week long conference in Pisa, Italy from June 26 to June 30, 2023. The topic of the conference is “Geometry and Analysis of Groups and Manifolds”. The conference involves participants and speakers from three different mathematical communities, namely geometric flow, analysis on metric spaces and geometric group theory, with emphasis on the connection between these fields. The goal is to create a conducive environment for collaborations between these different communities of mathematicians. The participation of early career US mathematicians in a major conference like this will help maintain and enhance the leading position of the US in mathematical science research in the relevant areas. The principal investigators and organizing committee will make a concerted effort to identify and support participants from under-represented groups in mathematics. The conference will hold poster sessions for early career mathematicians to present their works, and select some of them for short talks. This conference will also disseminate knowledge to the broader mathematical community as the organizers plan to record all the talks and put the recordings on the internet.In recent years, there have been strong interactions between questions in geometric analysis and low dimensional topology/geometric group theory. On one hand, questions and examples from low dimensional topology and geometric group theory have inspired rapid development in geometric analysis. On the other hand, analytic methods have been used to prove deep theorems in low dimensional topology and geometric group theory. There are several emerging new connections between these fields, like the recent work of Kleiner-Muller-Xie where they used ideas from the analytical side of geometric mapping theory to study rigidity and regularity of quasiconformal maps between certain spaces and groups, work of Kleiner-Lang where they used metric currents in geometric measure theory to study the large scale geometry of high rank analogues of Gromov hyperbolic spaces, work of Song on the spherical Plateau problem on group homology which connects a geometric variational problem with algebraic and topological properties of groups, etc. The goal of the conference is to bring together experts from these various different fields to exchange views and collaborate on important questions in these fields. More details can be found in the conference website: https://sites.google.com/view/geometryandanalysis/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.