Conference on Artin Groups, CAT(0) Geometry, and Related Topics

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This award provides partial support for participation by US-based mathematicians at the international conference "Artin Groups, CAT(0) Geometry, and Related Topics" to be held at the CIRM (Centre International de Rencontres Mathematiques) in Luminy, France from June 1-5 of 2020. This international meeting on geometric group theory is expected to have about 80-85 participants. The organizers will make a special effort to include a diverse group of graduate students and postdocs, and the program will incorporate mechanisms for encouraging their interaction with more established mathematicians. The subject of the conference can be broadly described as using geometric methods to study algebraic objects. More specifically, the idea is to study groups by realizing them as groups of symmetries of some space, then to use geometric features of the space such as curvature to draw conclusions about the group. This subject, called geometric group theory, has expanded dramatically in recent years and is now a major current in mathematics. This conference will highlight the interaction between two main themes in geometric group theory: Artin groups on the one hand, and CAT(0) geometry on the other. Perhaps the most well-known examples of Artin groups are the braid groups. The study of Artin groups touches on many different fields, including low-dimensional topology, singularity theory, algebraic topology, and mathematical physics. CAT(0) spaces were introduced as a synthetic analog of non-positively curved manifolds. The symmetry groups of CAT(0) spaces turn out to have strong algebraic properties, making them an ideal tool for geometric group theory. Although Artin groups and CAT(0) geometry and their strong relationship will be the unifying theme of the conference, related topics such as Coxeter groups, three-dimensional manifolds, automorphisms of free groups, and mapping class groups will also be included in order to enrich exchanges between participants and inspire ideas for new research projects. Details of the conference and registration information may be found at https://conferences.cirm-math.fr/2159.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.