He specializes in differential geometry. As of 2007, he has served as the chairman of the Mathematical Sciences Research Institute (MSRI). He is known for his work in exterior differential systems, special holonomy, and Finsler geometry.
Bryant surfaces, surfaces of unit constant mean curvature in hyperbolic space, are named after him.
The Bryant soliton is also named after him. In 2013 he became a fellow of the American Mathematical Society.
On February 1, 2015, he began his two-year term as president of the American Mathematical Society. South. South. L. O.