Brussels-London XXV

The geometry of phase transistions

Université Libre de Bruxelles, 30th January 2026

The event will take place in the Mathematics Department of Université Libre de Bruxelles. The talks will be held in the Salle Solvay, on floor 5 of building NO, Campus de la Plaine. Click here for a map of the campus as well as local travel instructions.

Most international visitors will arrive at Gare du Midi (where the Eurostar and Thalys terminals are). From here the easiest route to the ULB is by metro. Take line 2 or 6 in the direction "Elisabeth", and change at "Arts-Loi" for line 5, direction "Hermann Debroux", which will stop at "Delta". The journey should take approximately 30 minutes.

The event will begin with lunch from 12pm. Lunch is free for all registered attendees. It will take place in the Maison des Anciens, which is on Campus de la Plaine, a short walk from where the talks will take place. The restaurant is above the Forum, marked as "UAE" on the map linked to above. Note you have to walk up steps outside to get on to the top level of the Forum where the restaurant is.

The talks will be held in the Salle Solvay, 5th floor of building NO, are at 13.30, 14.50 and 16.10, with coffee breaks in between.

To attend this event, you must register in advance.

Joaquim Serra. Recent Progress on Stable Solutions of the Allen–Cahn Equation.

I will present recent results and open problems concerning stable solutions of the Allen–Cahn equation and its free boundary version. In particular, I will discuss the long-standing problem of classifying stable solutions to the Allen–Cahn equation, both with and without area bounds, in low dimensions, and the consequences of these classifications. I will outline the classical results and highlight more recent developments, emphasizing the main difficulties in the problem and some of the key ideas underlying the proofs of our recent results. The talk is based on two papers: one joint with Chan, Figalli, and Fernández-Real, and another joint with Florit-Simon.

Sylvia Serfaty. Vortex points and vortex lines in the Ginzburg-Landau model.

I will review work with Etienne Sandier and more recent joint work with Carlos Román and Etienne Sandier, where we study the onset of vortices in the two and three-dimensional Ginzburg-Landau model of superconductivity. We discuss the critical field at which the first vortices appear, the optimal number of lines, and Gamma-limit problems for their effective interaction and arrangement.

Etienne Sandier. Minimizing entire solutions to vector Allen-Cahn equations in R^2.

I will report on a joint work with Peter Sternberg and recent joint work with Lia Bronsard and Peter Sternberg, where we try to describe minimizing entire solutions to the vector Allen-Cahn equation with three wells in two space dimensions. It is known that the Gamma-limit by blow-down of this problem is a minimal partition problem with weights for which minimal cones are easily described. We will see that, depending on the weights, each minimal cone may, or may not, correspond to a minimizing entire solution.