9401428 Hochster This award supports research in commutative algebra and algebraic geometry. The principle investigator will continue investigating several long standing questions in the theory of Noetherian rings, to explore the relationship of these questions with the burgeoning theory of tight closure, including its relationship to absolute integral closures and to achieve a better understanding of the geometric significance of the condition on a ring that all of its ideals be tightly closed. The faculty associate will study primary decompositions of ideals, tight closure, mixed multiplicities, joint reductions and ideals generated by monomials in a system of parameters in a local ring. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry. ***
