NSF-CBMS Regional Conference Proposal #9414514 Joseph Brennan Abstract: Tight Closure, Big Cohen-Macaulay Modules and Uniform Artin-Rees The three topics listed in the title of these lectures have provided distinct yet suprisingly intertwined threads in commutative algebra. These lectures will provide a general presentation of these topics with a view towards examination of the relationship of the homological conjectures to the resolution of singularities, the Relation-Type conjecture, the strong uniform Artin-Rees conjecture, and the strong Macaulayification conjecture.
