This award supports work on two sets of major problems in commutative algebra. The principal investigator will work on Serre's conjecture on interesection multiplicity of modules and Chow groups of a complete ramified regular local ring. He will also work on the canonical element conjecture of Hochster and related problems. 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.
