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.

Title: The Precedence-Constrained Family Traveling Salesman Problem

Speaker:  Raquel Bernardino, Department of Mathematics, Lisbon School of Economics and Management (ISEG)

Date | Time: April 8, 2026 | 14h30

Place: NOVA FCT,

Abstract:

We introduce the Precedence-Constrained Family Traveling Salesman Problem (PC- FTSP), which generalizes the FTSP by adding precedence relations between families. The PC-FTSP arises in warehouse order picking with scattered storage, where heavier items must be picked before lighter ones. We propose several formulations and compare them theoretically and empirically. We also derive valid inequalities that strengthen the linear programming (LP) relaxations. As some formulations are non- compact, we design a branch-and-cut algorithm to solve them. Results show the non- compact formulations outperform the compact ones, and the inequalities effectively strengthen the LP bounds on our instances.