Professor Efrat will work on several problems connected with automorphic forms. In particular, he will study the interplay between dynamical systems on the unit interval and zeta functions attached to Riemann surfaces. In particular, to explore consequences of the connection between zeta functions of modular surfaces and the determinant of the transfer operator for the corresponding dynamical system. Automorphic forms arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory.
