Date/Time
Date(s) - 28/11/2025
1:30 pm - 2:30 pm

Speaker: Vincent Millot (Université of Paris Est-Créteil)

Location: Hamilton Hall, Room 410

Title: Torus and split solutions of the Landau-de Gennes model for nematic liquid crystals

Abstract: In this talk, I will present the Q-tensor model of Landau-de Gennes for nematic liquid crystals from the mathematical perspective. I will draw the main differences with respect to more usual Ginzburg-Landau theories in terms of the internal structure of ground states, at least in a parameter regime called  Lyutsyukov. regime. In this regime, the order parameter takes values in the 4-dimensional sphere S^4 and the potential well in the energy is a representation of the real projective plane in S^4. In the case where the 3D domain is the unit ball and the Dirichlet boundary data is radially symmetric, one may expect that an energy minimizer inherits such symmetry. Simulations show that this is not the case and a certain toroidal structure is expected to appear. If axial symmetry is imposed to reduce the complexity, another type of « singular » solution appears, the split solutions. By means of regularity results and algebraic representations of harmonic 2-spheres in S4, I will discuss the existence / geometry of torus and split solutions, and the dependence with respect to the shape of the domain. This talk is based on joint works in collaboration with Federico Dipasquale and Adriano Pisante.