Title: Interpolation between Closure Operations in Commutative Algebra

Abstract: Integral Closure has been an important feature of many algebraic fields of study since the nineteenth century. In commutative algebra it is often studied in conjunction with tight closure since both properties can be encoded via Hilbert functions. In a 2018 paper Dr. William Taylor outlines an interpolation amongst these closures. I will provide a background of the theory and a number of Dr. Taylor's results as well as some future directions the research could take and some thoughts I have on the main objects of study.