This award supports the research of Dr. Robert Kottwitz in Automorphic Forms. Among his projects are joint work with D. Shelstad involving a twisted form of the Trace Formula and its relation to twisted endoscopic groups. He will also investigate the spaces of points modulo p on certain moduli spaces, and work on a conjectured "Fundamental Lemma" in the field, according to which certain spherical functions have matching orbital integrals. 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 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.
