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Computer experiment played an important motivational role in Thurston's work, including the formulation of his (now proved) Geometrization Conjecture.
Ian Agol of the University of California at Berkeley describes a new proof of Dani Wise's Malnormal Special Quotient Theorem, which states that a special cubulated hyperbolic group may be filled along malnormal quasiconvex subgroups to get virtually special quotients, June 27, 2014 at the Bill Thurston Legacy Conference.
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.