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Non-arithmetic lattices

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NPC - Non-positive curvature group actions and cohomology

In 1980 Mostow found the first examples of non-arithmetic lattices in PU(2,1). More examples were found and Deligne and Mostow gave a list of examples in 1986. Work of McMullen, based on work of Kappes and Moeller, showed there are 9 commensurability classes of non-arithmeticlattices in PU(2,1) on this list. No new examples were found until my recent work with Deraux and Paupert. We have constructed 13 new commensurability classes. I will give a history of this problem and then outline our recent results.



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