William Kazez and Gordana Matic

William Kazez and Gordana MaticCreative Research MedalĀ 2012

William Kazez and Gordana Matic, professors of mathematics, are recognized as experts in a branch of mathematics called three-dimensional contact topology. They are particularly interested in three-dimensional manifolds, which are the possible global shapes of the three-dimensional space in which we live. The basic questions in two-dimensional geometry were answered long ago, but the basic structure of three- and four-dimensional objects has proven more difficult. Because human beings live in three dimensions, the understanding of these objects is of tremendous importance. In a series of five papers, Kazez and Matic resolved many longstanding difficulties in relating properties of contact structures to another popular approach used to analyze three-dimensional manifolds called open book decompositions. They also demonstrated a novel method of calculating an abstruse technical device known as Heegaard-Floer cohomology, a difficult and sometimes intractable method of analyzing basic topological information.