SEMINAIRE MERCREDI 22 SEPTEMBRE 2004 14 heures Salle Séminaire 5 Centre de Physique Théorique Marseille-Luminy Rafael Benguria Pontificia Universidad Catolica de Chile Title: An isoperimetric problem for curves on the plane and its connection to the Lieb-Thirring inequalities Abstract: In this talk I will make a connection between an open isoperimetric problem for closed curves on the plane and a conjecture of Lieb and Thirring for the sharp constant of the Lieb-Thirring inequalities with exponent 1. This is joint work with Michael Loss.