Conference: Geometry and Analysis of Groups and Manifolds

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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.