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Benson Farb of the University of Chicago describes his work on building a theory called "Representation stability/FI-modules," whereby various sequences of spaces stabilize when viewed through the lens of representation theory, June 23, 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.