Mathematical Sciences: The Twisted Trace Formula and Cubic Non Normal Extensions

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Professor Stopple will work on a new way to look at the trace of Hecke eigenforms on GL(3) by generalizing an idea of Zagier on the trace formula for Hecke operators. He will then apply this trace formula to the case of non-normal cubic extensions of the rationals. 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.