Certified symbolic-numeric algorithms for real algebraic geometry
Certified isolation of the real solutions of polynomial systems. Co-supervision with Elias Tsigaridas (Sorbonne Université & Inria Paris) is possible.
- Suitable for
- PhD thesis
- Supervision
- Tülay Ayyıldız
- Prerequisites
- Computer algebra; real algebraic geometry; numerical analysis
Isolating the real solutions of polynomial systems with guarantees is a central problem in real algebraic geometry. Symbolic methods are exact but slow, while numerical methods are fast but uncertified.
Goal
Develop certified symbolic-numeric algorithms for real solution isolation, building on Hermite matrices and rational univariate representations, with complexity analysis and implementation.