Mathematical Sciences: Shimura Varieties and Endoscopy

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Professor Kottwitz will work on several problems connected with automorphic forms. In particular, he will study endoscopy and its applications to Shimura varieties. He will also work on the stable version of Arthur's trace formula, problems of bad reduction of Shimura varieties and connections between the stable trace formula and the Lefschetz fixed point formula. 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.