Steepest Descents with Sobolev Norm (Lester Senechal).
The students in Senechal's 1990 group were Jill Kelly (Yale, '92), Lily Khadavi (Harvard, '91), Andrew Kresch (Yale, '93), Keith Slonski (Gettysburg College. '91), Irene Thomas (MHC, '93). The group continued the work of 1989, but with several new approaches. They mounted a general attack on extremization on manifolds in function spaces, applying spectral theory to establish prototypes for establishing the convergence of the processes in restricted circumstances. They also obtained some spectral estimates for operators on function spaces which extended Gershgorin's circle theorem to the infinite dimensional setting. Kresch presented a paper at the AMS-MAA 1991 special session on research by undergraduates.