This project involves work in several different areas of algebra. One area to be studied is the integral representations of Gl(n). Another area under investigation is the representation theory of artin algebras and the theory of lattices over higher dimensional orders, with special emphasis on Cohen-Macaulay approximations. Work will also be done on commutative algebra and algebraic geometry from the perspective of free resolutions and the theory of curves. The research involved in this project has great breath and covers some of the most significant areas of modern theoretical algebra. This includes commutative algebra and the integral representations of the general linear group; the structure theory of noncommutative rings and, in particular, the representation theory of artin algebras; and commutative algebra and algebraic geometry. These areas are of interest to many branches of mathematics.
