Project description: This project will investigate algebraic objects called nearly complete intersections (NCIs), defined by Boocher and Seiner in 2018. Recent (as yet unpublished) work by Miller and Stone characterizes NCIs graph theoretically, and our goal is to use the graph description to compute the free resolution of an arbitrary NCI. Early in the program we will become acquainted with free resolutions, NCIs, and their characterization as graphs. We will also gain some comfort using the computational algebra software Macaulay2. To get a head start on using Macaulay2, you can visit http://web.macaulay2.com and complete the tutorials (don't worry if some of the commutative algebra concepts are new to you while you're doing the tutorials!).

Expected background: Students are expected to have taken at least one course in abstract algebra and at least one course in linear algebra. Additional coursework covering modules and free resolutions is useful but not necessary.

Project faculty:
Prof. Courtney R. Gibbons, Hamilton College
Email: crgibbon at hamilton.edu (change "at" to "@")
Office hours: TBA
Bio: Gibbons is an associate professor of mathematics at Hamilton College who works on problems in commutative and homological algebra, many of which come from Boij-Soederberg theory. She received her BA in mathematics from Colorado College in 2006 and her MS and PhD in mathematics from the University of Nebraska-Lincoln in 2009 and 2013 respectively.