This award supports the research of Professor L. Walling to work in automorphic functions. She intends to study the Fourier coefficients of theta series attached to lattices arising from quadratic forms. She also intends to study the analogous situation over function fields. Modular 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.
