Mathematical Sciences: Topics in Analysis on Symmetric Spaces and Antomorphic Forms

Professor Katok will work on several problems connected with automorphic forms. In particular, she will study the Fourier coefficients of non-holomorphic Maass forms. She will also study a generalization of Livshitz theory through the development of a higher cohomology theory for hyperbolic dynamical systems. 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.