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. For example spin liquids, these exotic phases of matter that stubbornly refuse to order, often support long-range quantum entanglement, while their excitations take the form of fractionalised quasi-particles. This fractionalisation has been famously illustrated by the Quantum Hall effects, Majorana fermions in Kitaev materials, magnetic monopoles in spin ice, or fractonic matter, making contact with data storage in quantum information as well as yet unobserved high-energy phenomena. Its beauty is that each crystal, each model, comes with its own signature. A growing number of spin-liquid materials have been discovered in the XXIst century, making this topic one of the most active in quantum matter nowadays, supported by strong ties between experiments and theory. And thanks to the remarkable developments in moiré systems and Rydberg atoms over the past years, these questions have spread with impressive promises to synthetic platforms, bringing up new benchmarks to establish in understanding, scope, and challenges.

This school will take place at the Institut d'Etudes Scientifiques de Cargese (IESC), thanks to the support of CECAM and the IESC. Its goal is to form the next generation of students and postdocs on these topics, to give them a solid background on topological and quantum matter, advanced numerical methods and synthetic platforms, to become the actors of this progress. To do so we will bring together world experts, both to teach the latest developments taking place in these different fields of research and numerical developments, and to foster discussions between teachers, organizers and young researchers. Poster sessions will be organized for the participants.

All details for application and registration are given on the tab "Practical Information".
The deadlines are April 28^th, 2026 for application, and June 26^th, 2026 for registration (if your application has been accepted).

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

– Yasir Iqbal (Indian Institute of Technology Madras)
– Ludovic Jaubert (CNRS, University of Bordeaux)
– Siddharth Parameswaran (University of Oxford)
– Cécile Repellin (LPMMC, CNRS, Université Grenoble Alpes)
– Kirill Shtengel (University of California Riverside)