Preprints and Publications The arithmetic rank of the residual intersections of a complete intersection ideal with Manav Batavia, Taylor Murray, and Vaibhav Pandey to appear in International Mathematics Research Notices. IMRN, 20 pages. [arXiv] Lifting systems for finite length modules with Benjamin Katz, Nawaj KC, Andrew J. Soto Levins, and Ryan Watson submitted, 19 pages. [arXiv]