Prof/Deputy Head of Department

4 West 4.12

Dept of Mathematical Sciences

Email: a.h.dooley@bath.ac.uk

# Anthony Dooley

## Profile

Anthony Dooley has worked across a broad area of mathematical analysis. Analysis is that branch of mathematics which deals with continuous phenomena, and while its origins are in the study of physical phenomena, its current applications are widespread and include such diverse fields as economic and financial modelling, climate and weather prediction, computer networks, not to mention quantum mechanics and relativity theory.

His interests in the theory of Lie groups spring from a fascination with the study of quantum mechanics, and how the geometry of the universe can be used to predict the particles which can exist. The groups which describe the symmetries of these geometries were studied by Lie in the late 19th century, and by now form a major part of modern mathematics. Analysis of these groups can be seen as a far-reaching generalisation of Fourier analysis and Dooley has extended familiar results to this wider setting, involving approximation theory, reconstruction methods, differential operators, random processes, and representation theory.

Dooley also works in the area of dynamical systems, which evolved from Statistical Mechanics to become a mathematical study of how systems evolve as time elapses. The area known as ergodic theory (from the Greek ergos, meaning work) has grown through the development of such notions as entropy and orbit equivalence, and now can be used to model the development of chaos, or progression to some kind of predictable limit in a variety of applications. Dooley has made significant progress in the understanding of non-singular dynamical systems, those where the size (or measure) of a set may vary with time. He has also worked on the study of systems of completely positive entropy, which display the most chaotic behaviour.