ANR Project: STOIQUES Shape and Topology Optimization: Impactful QUestions and Emerging Subjects   Institut Élie Cartan de Lorraine           SAMM : Statistique, analyse, modélisation multidisciplinaire      Laboratoire Jean Kuntzmann           Laboratoire de Mathématiques et de leurs Applications de Pau Project summary. We are currently proposing an ANR project dedicated to the investigation of modern problems in shape optimization, which is currently inspiring multiple challenges. The main objective is to federate the community of researchers interested in this field, in order to develop new methods and tools for tackling new models or considering new constraints. We intend to focus our efforts on four main themes: (1) the study of new models involving nonlinear PDEs and topological constraints on domains; (2) the development of methods for establishing quantitative geometric inequalities. (3) Taking account of uncertainties in inverse problems involving shapes. (4) Developing original numerical approaches to avoid the use of costly meshes. The consortium has been put together in such a way as to emphasize the fundamental, applicative and numerical aspects, which are totally complementary and interconnected within this framework. Team members (PI in red, local coordinators in blue). Université de Pau et des Pays de l’Adour: Samuel AMSTUTZ - Fabien CAUBET - Julien DAMBRINE - Marc DAMBRINE - Enea PARINI - Charles PIERRE - Morgan PIERRE Université Grenoble Alpes: Eric BONNETIER - Matthieu BONNIVARD - Elie BRETIN - Dorin BUCUR - Charles DAPOGNY - Roland DENIS - Simon MASNOU - Mickaël NAHON - Edouard OUDET Université Paris 1: Grégoire ALLAIRE - Beniamin BOGOSEL - Blanche BUET - Antonin CHAMBOLLE - Gisella CROCE - Michael GOLDMAN - Jimmy LAMBOLEY - Idriss MAZARI - Bruno NAZARET - Nikita SIMONOV Université de Lorraine: Antoine HENROT - Antoine LEMENANT - Benoît MERLET - Grégoire NADIN - Marc PEGON - Yannick PRIVAT Meetings. May 5-6-7, 2025 (Grenoble) ; November 12-13-14, 2025 (Paris 1 or Nancy) ;