Daniel Biss is interested in topology and its connections with other areas of mathematics, especially algebraic geometry, Lie theory, and combinatorics. His thesis research is connected with the problem of finding a combinatorial formula for the rational Pontrjagin classes of a manifold. In particular, he has shown that the tangent bundle of a smooth manifold can be encapsulated in the combinatorial language of oriented matroids; this work is part of an ongoing program to apply oriented matroids to the study of differential topology. He also has a continuing interest in mathematical exposition, and is currently writing a book whose goal is to communicate the spirit of mathematics to a lay audience in an entirely non-technical manner.
Daniel Biss is a Clay Research Fellow from May 1, 2002 to June 30, 2007.