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
- Major: Mathematics, Physics
- Sponsor: Pergo SURF fellow
- Mentor: Constantin Teleman, Pablo Solis, Mathematics