Citation | The central part of Burt Totaro's work has been devoted to the interaction between two of the major areas of pure mathematics, topology and algebraic geometry. Inspired by the Hodge conjecture, Totaro has worked to uncover the fundamental topological structure of algebraic geometry. Each step has made possible the solution of a well-known problem in algebraic geometry and demonstrated that progress towards the Hodge conjecture will come through topology. Totaro's work has influenced a large group of algebraic geometers to use deeper topological methods in their work. His ideas have also had unexpected payoffs in a wide variety of other mathematical fields, including representation theory, Lie groups and group cohomology. |