Masterclass MINT 02/04/2026

jeudi 2 avr. 2026, 12:15 → 13:15 Europe/Paris

Amphithéatre Schwartz (Institut de Mathématiques de Toulouse (IMT))

Orateur : Radu Ignat (IMT)

Title : Vortex analysis in variational models.

Abstract: Vortices are topological singularities that appear in many physical systems (superconductivity, superfluids, ferromagnetics, liquid crystals etc.) We will present the analysis of vortices in a two dimensional Ginzburg-Landau (GL) model that is the prototype in several variational problems. This toy model depends on a small parameter epsilon and it is related to the harmonic map problem for unit length vector fields as epsilon tends to 0.
We will study ground states of (GL) for a given boundary data that carries a topological charge and induces the nucleation of vortices. Several mathematical tools will be introduced for this study such as the topological degree, the jacobian of the ground state (detecting the vortices) as well as the renormalized energy between vortices (determining their optimal location).