Seminar

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Tight closure theory is prominent to prime characteristic commutative algebra. Historically, tight closure has been used to simplify proofs of landmark theorems in commutative algebra, provide tests to determine when an element of a ring belongs to a particular ideal, and provides proofs of results in prime characteristic which otherwise can only be proved in equal characteristic 0. The first half of the talk will be devoted to basic definitions, properties, and consequences of tight closure. The second half of the talk we will go over several important classes of rings defined via tight closure, recent progress on the weak implies strong conjecture appearing in a joint paper with Ian Aberbach, and a conjecture that certain symbolic Rees algebras are Noetherian.

On The Weak Implies Strong Conjecture And Finite Generation Of Symbolic Rees Algebras