mercredi 4 nov. 2026, 12:15 → 13:15

Amphi Schwartz (1R3) (Institut de Mathématiques de Toulouse (IMT))

Title : The geometry of liquid crystals

Speaker: Xavier Lamy 

In a typical liquid crystal, elongated molecules tend to align. This can be modelled by a unit vector field indicating the direction of alignment, and minimizing, locally, the Dirichlet energy (integral of its gradient squared). This is a special case of classical geometric objects called harmonic maps, a generalization of geodesics. Unlike geodesics, they might not be smooth, but singularities can be described quite precisely: here, it turns out they all look like x/|x|. I will explain some of the ideas behind this fact, as well as open questions.