Complex Hyperbolic Lattices

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This project involves building fundamental domains for lattices of complex hyperbolic isometries. This topic goes back (at least) to seminal work of Mostow in 1980 and more recently substantial progress has been made by Deraux, Falbel, Parker and Paupert as well as their students and co-authors. One theme that runs through all these projects is the interaction between theoretical constructions and computer experiment and verification. In this project, Julio Quijas will extend earlier constructions to lattices generated by three complex reflections of different orders, and he will also attempt to classify all possible constructions of this form.