- About Mutations of Laurent Polynomials
- Project Year:
2025
- REU Student (s):
Kyan Valencik | Rutgers University-New Brunswick NJ
- Student 1 Institution:
Rutgers University-New Brunswick
- Project Mentor:
Christopher Woodward
- Project Mentor Area:
Mathematics
- Project Abstract:
In the subject of mirror symmetry, there is believed to be a correspondence between Fano varieties and Laurent polynomials. In their paper Maximally Mutable Laurent Polynomials, Coates et al. proved that a family of Fano three-manifolds correspond one-to-one with certain mutation classes of Laurent polynomials. Here, a mutation is a change of variables which changes a Laurent polynomial \(f\) into another Laurent polynomial \(f\). The mutation graph is the graph whose vertices are all Laurent polynomials produced in this way, and edges are the mutations. In our project we will examine the mutation graph of the Laurent polynomial \(x+y+z+\frac{1}{xyz}\) corresponding to projective three-space \(\mathbb{P}^3\).
