Keith Burns works on geometrical and dynamical problems connected with geodesics in manifolds with nonpositive curvature. Recent work has concentrated on partial hyperbolicity and stable ergodicity.
Manifolds of nonpositive curvature and their buildings, coauthor R. Spatzier, Mathematiques de l'Institut des Hautes Etudes Scientifiques, 65 (1987), 35--59.
On topological Tits building and their classification, coauthor R. Spatzier, Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, 65 (1987), 5--34.
Ergodic geodesic flows on product manifolds with low dimensional factors, coauthor Marlies Gerber, Journal fur die reine und angewandte Mathematik, 450 (1994), 1--35.
On the ergodicity of partially hyperbolic systems, coauthor Amie Wilkinson, Annals of Mathematics, 171(2010), 451--489.
The Weil-Petersson geodesic flow is ergodic, coauthors Howard Masur and Amie Wilkinson, Annals of Mathematics, 175(2012), 835-908.