Priya Kshirsagar
An algebraic variety is a generalization of a solution set to a family of polynomial equations. De Concini and Procesi developed a canonical method of compactifying any symmetric variety. This resulting compactification, called the wonderful compactification, has many favorable algebraic and geometric properties. Alexeev and Brion developed a method of degenerating any spherical variety to a toric variety. Many tools, such as combinatorics, can be used to study toric varieties in great detail. Thus, my main goal is to develop and study toric degenerations of the wonderful compactification. Eventually, I […]
Sean Sun
Cholesterol is an essential molecule to survival. Some of its functions include being a precursor to steroid hormones, a component of cell membranes and cell signalling. Without cholesterol, we would lose control of blood pressure and our body’s cells would fail to acquire nutrients necessary for survival. My project investigates Smith-Lemli-Opitz Syndrome (SLOS), which is an inborn error of cholesterol synthesis. Because only one non-functional gene causes SLOS, we can apply gene therapy to integrate a functional gene into the genome of a SLOS cell. To date, we have improved […]