Vladimir Voevodsky is known for his work in the homotopy theory of schemes, algebraic K-theory, and interrelations between algebraic geometry and algebraic topology. He made one of the most outstanding advances in algebraic geometry in the past few decades by developing new cohomology theories for algebraic varieties. Among the consequences of his work are the solutions of the Milnor and Bloch-Kato Conjectures. More recently, he was interested in type-theoretic formalizations of mathematics and automated proof verification, and was working on new foundations of mathematics based on homotopy-theoretic semantics of Martin-Löf type theories.
Fields Medalist, 2002