Deformations of solutions of differential equations

Mercedes HAIECH
Université de Limoges
http://perso.eleves.ens-rennes.fr/people/Mercedes.Haiech/

Date(s) : 06/01/2022   iCal
14 h 00 min - 15 h 00 min

Given an algebraic differential equation (or system) we can be interested in the geometrical object defined by the set of its solutions. In algebraic geometry, the study of the geometry of the solutions of a polynomial equation gives information about the singularities of this equation. If we transpose some of these algebraic invariants into the differential world, we can wonder what information they give about the differential equation. In this presentation, we will study the behavior of the formal neighborhood of a fixed solution of the differential equation. In our framework, this object can also be understood as the space of deformations of this solution.

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