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Thurston had a longstanding interest in understanding geometric and topological properties of arithmetic hyperbolic manifolds. For example in his 1982 Bulletin Article, as Qn 19 of the problem list, Thurston posed: "Find topological and geometric properties of quotient spaces of arithmetic subgroups of PSL(2,C). These manifolds often seem to have special beauty." Alan Reid of the University of Texas at Austin discussed this theme, including recent work and future directions, at the Bill Thurston Legacy Conference, June 23, 2014.

The conference, "What's Next? The mathematical legacy of Bill Thurston," held at Cornell June 23-27, 2014, brought together mathematicians from a broad spectrum of areas to describe recent advances and explore future directions motivated by Thurston's transformative ideas.