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Posts

On the equations of Poizat and Liénard

An electronic circuit described by an equation of Liénard. Abstract: We study the structure of the solution sets in universal differential field...

The degree of nonminimality is at most two

Abstract : It is shown that if $$p$$ is a complete type of Lascar rank at least 2 over $$A$$, in the theory of differentially closed fields of charact...

Abelian reduction in differential-algebraic and bimeromorphic geometry

Abstract : Several results on the birational geometry of algebraic vector fields in characteristic zero are obtained. In particular, (1) it is shown that...

When any three solutions are independent

Abstract: Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any numb...

Generic planar algebraic vector fields are strongly minimal and disintegrated

Representation of a complex hyberbolic singularity. Abstract: In this article, we study model-theoretic properties of algebraic differential equa...

Relative internality and definable fibrations

Abstract: We first elaborate on the theory of relative internality in stable theories, focusing on the notion of uniform relative internality (called collaps...

Rational factors, invariant foliations and algebraic disintegration of compact mixing Anosov flows of dimension 3

An Anosov flow of dimension three. Abstract: In this article, we develop a geometric framework to study the notion of semi-minimality for the gen...

Corps différentiels et flots géodésiques I: Orthogonalité aux constantes pour les équations différentielles autonomes

A weakly-mixing discrete dynamical system. Abstract: Orthogonality to the constants is property of an algebraic differential equation that origin...

Differential fields and Geodesic flows II : Geodesic flows of pseudo-Riemannian algebraic varieties

Abstract: We define the notion of a smooth pseudo-Riemannian algebraic variety $$(X,g)$$ over a field $$k$$ of characteristic 0, which is an algebraic an...

Geodesic Flows and Model Theory of Differential Fields

Abstract: This thesis is dedicated to studying the interactions between two different approaches regarding differential equations: the model-theory of differ...

talks

Conference Model Theory and Applications

Title : Disintegrated differential equations and mixing Anosov flows. Vidéo , Slides

Title :