This award supports the research in automorphic forms and representation theory of Professor Freydoon Shahidi of Purdue University. One of Dr. Shahidi's projects is to study the possible equivalence, for a cusp form on a quasi-split group over a number field, between having a non-zero Fourier coefficient with respect to a generic character of a maximal unipotent subgroup, and having generic local components everywhere. Another related project is to prove the holomorphy of certain local L- functions related to tempered representations. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of modular and automorphic forms is one of the most active. 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.
