Research Interests

My interests and work concern various areas relating mathematics and physics. I was part of the effort that created a mathematically rigorous theory of equilibrium statistical mechanics. This is the study of infinite systems of particles at a given temperature, and of the changes (phase transitions) that occur when the temperature is varied. I also participated in the effort to understand chaos. Chaotic time evolutions, like those occurring in hydrodynamic turbulence, are deterministic but irregular and of limited predictability. The problem here was to make sense of the experimental data and to create an appropriate mathematical theory for their description. The necessary mathematics is part of smooth dynamics and ergodic theory. These same mathematical theories are also needed to understand nonequilibrium statistical mechanics, which is the theory of irreversible processes, like heat diffusion and also the multiple processes of life. This is my current domain of interest. As a sideline, I have pondered the relations between physics, mathematics, and the structure of the human brain. How different, for instance, could be the mathematics of alien intelligent species?

Membership Type

International Member

Election Year


Primary Section

Section 13: Physics

Secondary Section

Section 11: Mathematics