Research  |  Accomplishments

Smoller has written over 150 research papers, (including 21 in the last 5 years). He has won many awards, including a Guggenheim Fellowship, a senior Humboldt Fellowship, and was awarded the prestigious GD Birkhoff Prize in Applied Mathematics for 2009.

The citation for the Birkhoff Prize states that he was awarded the prize for his leadership, originality, depth and breadth of work...and for his powerful intuition for innovative new directions and his forcefulness in cementing powerful collaborations that have been emblematic of a career worthy of emulation.

His book, Shock Waves and Reaction-Diffusion Equations (1984) has had a far-reaching impact on both fields, and has remained for a long time the standard source in these fields. One of the topics expounded there is Smoller's work with Conley which introduced topological techniques to reveal the general structure of shock waves.

Smoller's research work is very wide. It covers partial differential equations, dynamical systems, fluid mechanics and magnetohydrodynamics, in particular shock wave theory, general relativity, the Yang-Mills equations of non-Abelian gauge theories, decay and stability of solutions of various force fields in the Kerr (rotating) background geometry, and existence and nonlinear stability of rotating Newtonian stars. He has also done work in mathematical biology. Smoller is usually not content with works of a technical nature which only improve known results, but rather he seeks new directions in uncharted territory.