9700682 Aberbach This award supports work on several problems in commutative algebra. These include studying Huneke's relation-type conjecture for parameter ideals, localization of parameter test ideals, and localization of tight closure in general. 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.
