Supervision : Mohab SAFEY EL DIN

Connectivity in semi-algebraic sets: algorithms, implementations and applications.

The goal of this PhD thesis is to design theoretical tools and to develop algorithms using them to solve connectivity problems on semi-algebraic sets. We rely on the concept of roadmaps which is a one-dimensional subset preserving the same properties of connectedness. Constructing roadmaps and knowing how to use them are the two major issues of this PhD thesis.

2022-2023 Publications

• 2023
  • N. Islam, A. Poteaux, R. Prébet : “Algorithm for connectivity queries on real algebraic curves”, (2023)
• 2022
  • D. Chablat, R. Prébet, M. Safey El Din, D. Salunkhe, Ph. Wenger : “Deciding Cuspidality of Manipulators through Computer Algebra and Algorithms in Real Algebraic Geometry”, ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, Lille, France (2022)
  • R. Prébet, M. Safey El Din, E. Schost : “Computing roadmaps in unbounded smooth real algebraic sets I: connectivity results”, (2022)