This award to the University of California at Los Angeles supports the Los Angeles Number Theory Group, a research activity in the category of Mathematical Sciences Research Groups. The four principal members of the Group are Professors Haruzo Hida, Jonathan Rogawski, and Don Blasius of the University of California, and Professor Dinakar Ramakrishnan of the California Institute of Technology. The purpose of the award is to make possible visits to the greater Los Angeles area by outside researchers in the field of automorphic forms and 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.
