- Project Year:
2020
- REU Student (s):
Anna Antal | Rutgers University-New Brunswick NJ
| Samuel Panitch | University of Pennsylvania PA
- Student 1 Institution:
Rutgers University-New Brunswick
- Student 2 Institution:
University of Pennsylvania
- Project Mentor:
Christopher Woodward
- Project Mentor Area:
Mathematics
- Project Abstract:
In this project, we explored the notion of polynomial mutation in the context of algebraic geometry. It is conjectured that these polynomials can tell us something about the smoothing components of deformations of toric varieties. We worked on a simple combinatorial proof that an irreducible 0-mutable polynomial is rigid maximally mutable. An algorithm for reducing polynomials was developed, although it was demonstrated that such an algorithm cannot be guaranteed to find 0-mutable polynomials efficiently. Finally, we considered different notions of polytope mutation, and proved an equivalence between different definitions. Using this equivalence, we showed a fact about the number of possible mutations of a polynomial, up to isomorphisms of the mutations' convex hulls.
