Professor Craig Huneke, University of Kansas
This talk will describe some basic problems in commutative algebra, whose solution requires a method called reduction to characteristic p. This method has been codified in a theory called 'Tight closure'. We will outline the main steps in reduction to char. p, and illustrate on some of the problems. These problems include understanding rings of invariants of groups acting linearly on polynomial rings, and questions concerning the behavior of polynomials which vanish to prescribed multiplicities at points in the projective plane. Almost no advanced knowledge beyond a course on rings, groups, and fields will be assumed.
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