Priya Kshirsagar L&S Sciences
Toric degeneration of the wonderful compactification
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 will compare properties of the degeneration and those of Gelfand-Zeitlin integrable systems. This may have applications in mirror symmetry.
Message To Sponsor
I am so grateful for this wonderful research opportunity through the Pergo Foundation. I feel especially fortunate to have received funding to work on a project in math, especially one which is so difficult to motivate and explain to others. Beginning a project in math is a rather daunting task, especially for undergraduates like me who have only just learned the fundamentals. I am extremely grateful for my advisors, Pablo Solis and Constantin Teleman, for dedicating so much time and patience to guide me. After this summer, I plan to continue research in mathematics.