Current research program : Prime Rigidity Theory (PR)

 

EMA School 

 

Thesis

(2016): Coupled systems morphogenesis and self-organization in biological systems. 

Advisor: Pr. Philippe Thieullen 

The main points of the thesis. English version   PDF (05/06/2025). Cambridge Open Engage. doi:10.33774/coe-2025-170lk   

 

Publication

 (2024): Exponential stable manifold for the synchronized state of the abstract mean field system. Journal of Applied Nonlinear Dynamics .

 (2023): Ordinary differential equations defined by a trigonometric polynomial field. Dynamical Systems Journal.

 (2018): [with Pr. Thieullen and A. Kessi] Invariant cone and synchronization state stability of the mean field models. Dynamical Systems Journal.

 (2017): [with A. Kessi and Pr. Thieullen] Synchronization hypothesis in the Winfree model. Dynamical Systems Journal.

 

 

Working papers

 (2026): (Root) Rigidity and Structural Asymmetry of Bounded Solutions. 

 (2026): (Bridge) Asymmetry and the Riemann Hypothesis. 

              or, Scalar rigidity, abstract prime systems, and the Riemann zeta function.

 (2026): (Deduction of the Theory) Euler products from abstract prime systems and rigidity. 

 (2026):  Bounded solutions of a complex differential equation arising from the Riemann zeta function. 

 (2026):  When Periodicity Fails to Guarantee the Existence of Rotation:

               A Counterexample on the 3-torus with a Nilpotent Linearization.

 (2026): Rigidity and Spectral Asymmetry for Operators in Linear Dynamics. 

 (2026): On a Rigidity Equality for Bounded Solutions: Request for Counterexamples. 

 (2026): Holomorphic Wronskian for abstract rigidity inequalities. 

              Numerical Simulation with the Classical Wronskian:

              https://colab.research.google.com/drive/1ICP-fBZgE9t3elHp9X4B5BqhnraEQJKS?usp=sharing

 (2019): Synchronization in abstract mean field models. 

 

Oral Presentation

SIMBAD: Séminaire Itinérant de Mathématiques, Biologie et Applications. 24 mai 2016, Paris (France).

GDR: Journées du GDR AFHP, Institut de Mathématiques, Université de Bordeaux. October 9-11, 2017 (France).

AquiDOC: Valoriser son doctorat en cotutelle dans sa poursuite de carrière, 19 Octobre 2017, Université de Bordeaux (France).

CMA'2018: Invariant and positive resolvent matrix: Stability and application. Congrès des Mathématiciens Algériens, 12-13 mai 2018, Boumerdès (Algérie).

 

PhD supervisor: (2026). (co-supervised with Prof. Ph. Thieullen) of Ms. Rosa Bedjou.

Thesis title: Machine Learning through Synchronization of Coupled Oscillators.

 

Poster

Poster: PDF - "Periodic locked orbit in Winfree Model with N oscillators" (2015).

 

Course

Course of differentials equations for BSc (License). Ebook