9 Mars 2026 Luca Nenna et Martin Rakovsky

lundi 9 mars 2026, 10:00 → 12:00 Europe/Paris

Maryam Mirzakhani (Institut Henri Poincaré)

 

Martin Rakovsky(LMO-Orsay)

 

Title : Critical points of the two-dimensional Ambrosio-Tortorelli functional with convergence of the phase-field energy

 

Abstract : According to the variational approach to fracture introduced by Francfort and Marigo, the Mumford-Shah energy MS is commonly used to modelize brittle cracks in an elastic material. Ambrosio and Tortorelli proposed a variational phase field regularization AT of this functional which, through a Gamma-convergence result, leads to the convergence of global minimizers. This result gives however no information about the limiting behavior of general critical points.

 

Babadjian, Millot and Rodiac proved the convergence of critical points of the Ambrosio-Tortorelli functional to a critical point of the Mumford Shah functional, in the sense of inner variations, under the additional assumption of the convergence of the Ambrosio-Tortorelli energy to the Mumford Shah energy. In this talk, focusing on the two-dimensional setting, we extend this result under the sole convergence of the phase-field energy to the length energy term in the Mumford-Shah functional.

 

We investigate the limit measure T of the inner variations of AT. When comparing the limit of the Dirichlet part of AT with the elastic energy of MS, the defect measure that arises proves to remain singular with respect to Lebesgue. Moreover, we compute the singular part of T applying a result of De Philippis and Rindler.

 

Luca Nenna(LMO-Orsay)

Title: A convexity conjecture in quantum chemistry and  optimal transport 

 

Abstract: I will describe a famous conjecture, dating back from the 1980s, concerning the way that the electronic energy of an atom or a molecule depends on the number of electrons. Together with Simone Di Marino (Genova) and Mathieu Lewin (CNRS and Paris-Dauphine), we found the first counter-example by going to the semi-classical limit and studying an optimal transport problem. Our nuclei have a fractional charge and the conjecture remains open for integer charge systems, however.