Christopher D. Hacon
University of Utah
Mathematical and Physical Sciences
Mathematics, Applied Mathematics, and Statistics
Over the past ten years, working with McKernan and others, Hacon settled the main open questions concerning the geometry of higher dimensional complex algebraic varieties. More specifically, he and his coworkers essentially extended to all dimensions the birational classification of algebraic surfaces and threefolds due respectively to the classical Italians and to Mori. Consequences of Hacon's work include the finite generation of the canonical ring of all algebraic varieties, and the existence of moduli spaces for varieties of general type in any dimension. More recently, Hacon has opened new directions for the field by studying analogous questions in characteristic p > 0.