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"In June of 2014, a conference was held in William Thurston's honor called "What's Next? the mathematical legacy of Bill Thurston." This volume includes papers from conference presenters and solicited papers by prominent scholars. The papers are based on Thurston's fundamental contributions to topology, geometry, and dynamical systems. Beyond these specific accomplishments, they discuss how he introduced new ways of thinking about and of seeing mathematics that have had a profound influence on the entire mathematical community - Thurston discovered connections between disciplines that led to the creation of entirely new fields. This book brings together mathematicians from a broad spectrum of areas to describe recent advances and explore future directions motivated by Thurston's transformative ideas"--