This CECAM scool will take place at the "Institut d’Etudes Scientifiques de Cargèse" (IECS) in Corsica, France.

Looking at the frontier of contemporary physics, several aspects of condensed matter and ultracold atoms research have surfaced where fractionalisation, topological order and emergent gauge fields play a pivotal role. There is no doubt that the coming years will witness a worldwide surge of efforts at the interface between quantum matter and synthetic platforms, from fundamental physics to applications and algorithm development. The possible outcomes are numerous and promising, but a solid background across different topics from communities that do not necessarily talk to each other will be key. It is the goal of this school to form the next generation of researchers, to give them a solid background on topological and quantum matter, advanced numerical methods and synthetic platforms, to become the actors of this progress.

There will be 6h lectures given by:
- John Chalker (Oxford): Emergent gauge field theory and fractionalisation in many-body systems
- Paul Fendley (Oxford): The basics of non-invertible symmetries
– Antoine Browaeys (Saclay): Rydberg atoms
– Sylvain Ravets (Saclay): Optics in microcavities & topological photonics
- Rhine Samajdar (Princeton): Synthetic platforms and programmable quantum simulators 
- Frank Pollmann (Munich): Advanced numerical methods, including deep learning

Together with 1h lecture on focused topics by:
– Flore Kunst (Erlangen): Topology of non-Hermitian systems
– Rebecca Ribeiro-Palau (Saclay): Moiré materials
– Pieter Claeys (Cambridge): Quantum circuits
– Nick Bultinck (Ghent): Moiré materials
– Romain Vasseur (Geneva): Quantum Dynamics and Measurements
– Paul McClarty (Saclay): Altermagnetism