This research will deal with a number of problems in matrix theory and algebraic geometry. In matrix theory work will be done on estimating permanents of nonnegative matrices, comparing permanents of positive definite matrices with other generalized matrix functions, Knaster's conjecture for quadratic functions, matrix aspects of graph isomorphisms, and invariants of finite dimensional algebras. In algebraic geometry work will be done on the two dimensional Jacobian conjecture, the Riemann-Hurwitz formula for compact algebraic surfaces, and the uniqueness of Henon's form under diffeomorphism. This research focuses on two different areas: matrix algebra and algebraic geometry. The breadth of the research is one of the appealing aspects of the project. Friedland brings to bear his extensive knowledge of these two areas on each other to produce some very original work. Results of great value will be the result of this research.
