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Personnal mathematical notes and presentations

• Master thesis (DOI: 10.5281/zenodo.6634769) (french): Thesis on the subject of reduction of Children drawings and trees. We gice here a criterion of good reduction for trees: a tree without have good reduction if it has good reduction at one critical point wisely ramified.
• Presentation - Master thesis (french): Presentation of the Master thesis
• Semi-stable model of Belyi children's drawings (DOI: 10.5281/zenodo.6427559): in this note we continue the work of M. Zapponi on semi-model of children's drawing by applying it on Belyi childrens drawing. You can see the effective construction of model here.
• Factorisation of $X^n-\alpha$ over finite fields (DOI: 10.5281/zenodo.6789182): in this note we inspect the order of the irreducible factors of the polynomial $X^n-\alpha$ in finite fields $\mathbb{F}_p$.
• Factorisation of $X^n-\alpha$ over finite fields - II (DOI: 10.5281/zenodo.6916423): In this note we explain factorisation of polynomials $X^n-\alpha$ with factor grouping irreducible polynomials of same order. We give a method to find this factorisation by induction.
• Presentation - Factorisation of Belyi like polynomial over finite fields (DOI: 10.5281/zenodo.6634838): we explain here a method of factorisation for Belyi like polynomials in finite fields, based on a lattice method.
• Inséparabilité/Profondeur d'un modèle d'arbre: On décrit les nombre $\iota(\beta)$ associé à des modèles d'arbres polynomiaux et primitifs.
• Première exploration arithmétique de l'arbre de Bezout: Premiers questionnements et premiers résultats, entre autres la détermination des arbres de Bezout à bonne réduction.
• Etude des sources de l'article de Zapponi sur la spécialisation des arbres.

Maths programs

• For plotting children drawing: here
• Automatic calculation of semi-stable model for Belyi children drawings: here
• Show all the lattice of polynomials of given order modulo p: here

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