Computational Initiative in Core Mathematics

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The Department of Mathematics at the University of Michigan will hire a technical programmer whose responsibilities will be to assist faculty members and graduate students in research- related programming tasks which are special to mathematical interests, and to perform routine system administration tasks for the SUN and APOLLO computers. In addition, the Department will purchase a maintenance contract for its core SUN system. The research of the principal investigators is summarized below: The combinatorics group will use SUN work-stations to study classical groups and their Weyl groups. Directions will include a study of the Kazhdan-Lusztig representations on Sn and a comparison of algorithms for manipulating representations of classical groups. The nonlinear wave motion group will pursue several projects centered on the study of partial diffferential equations that are associated with wave propagation. In addition, a computer algebra program will be used to assist in doing computations with matrix-valued algebraic functions which are necessary to solve a large set of difference equations. The number theory group will use computing equipment to numerically approximate the special values of p-adic L-functions, resolve plane curve singularities by symbolic manipulation and calculate the coordinates of multiples of rational points as Jacobians of curves of genus two.