Conference on Aspects of Non-Positive and Negative Curvature in Group Theory

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This award provides partial support for participation by US-based mathematicians at an international conference on geometric group theory to be held at the CIRM (Centre International de Rencontres Mathematiques) in Luminy, France from June 17-21 of 2019. The conference will bring together a diverse group of approximately 120 mathematicians from the US, Europe and Asia. Along with twenty-two plenary lectures there will be a session of lightning talks where early career mathematicians will have the chance to present their work. This award will support the attendance of approximately 30 US-based mathematicians at the conference. Geometric group theory is a relatively recently recognized subfield of mathematics emerging from Gromov's work in the 1980s, which put the classical treatment of groups as geometric objects in a far broader context. The field is now quite large, and has interactions with many different fields of mathematics including low-dimensional topology, the topology of manifolds, complex dynamics, combinatorial group theory, logic and the study of various classical families of groups. The central idea of geometric group theory is to study a group through an action (typically an isometric one) on some space (typically a metric space) and then use properties of the space to deduce properties of the group. Perhaps the most successful instance of this is when the space has some form of negative curvature. While classically curvature is a concept of Riemannian geometry, another central insight of Gromov is that many properties of spaces of negative curvature in Riemannian geometry have "coarse" analogues and that this is the natural setting to study the geometry of groups. The study of groups that act on spaces with coarse versions of non-positive and negative curvature will be the focus of this week long conference. More information on the conference can be found at https://conferences.cirm-math.fr/1958.html.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.