Research Works

Ongoing Works

  • Non-negative forms on genus one curves, with G. Blekherman and R. Sinn.
  • Volumes computation through moments and holonomy, with J. Berthomieu and P. Lairez.
  • An Effective Positivstellensatz for Finite SemiAlgebraic Sets, with T. Krick and B. Mourrain

Preprints

  • On Łojasiewicz Inequalities and the Effective Putinar’s Positivstellensatz, with B. Mourrain and A. Parusiński [arXiv]
  • Exact Moment Representation in Polynomial Optimization, with B. Mourrain [arXiv]

Journal Publications

  • Degree Bounds for Putinar's Positivstellensatz on the hypercube, accepted for publication on SIAM Journal on Applied Algebra and Geometry, with L. Slot [arXiv]
  • On the effective Putinar’s Positivstellensatz and moment approximation. Mathematical Programming 200, 71–103 (2023), with B. Mourrain [arXiv][journal]

Conference Papers

  • Computing Real Radicals by Moment Optimization, ISSAC 2021: Proceedings of 46th International Symposium on Symbolic and Algebraic Computation, 43–50 (2021), with B. Mourrain [arXiv][conference]

Other Works

  • Non-negative forms on cubic curves, extended abstract in Oberwolfach Report no. 15, 2023 [report]
  • Degree bounds for Putinar’s Positivstellensatz on the hypercube, extended abstract in Oberwolfach Report no. 14, 2023 [report]
  • Effective Representations in Real Algebraic Geometry and Polynomial Optimization, Ph.D. thesis [manuscript]