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Liouville quantum gravity and the conformal bootstrap |

Remi Rhodes (Aix-Marseille University) and Vincent Vargas (University of Geneva) |

We present a rigorous probabilistic construction of Liouville Conformal Field Theory (LCFT). Then we explain how to derive the bootstrap formulae for this CFT via Segal’s axioms, hence bridging the gap between probability theory and representation theory for LCFT. In particular, we explain how to identify its 3-point correlation functions (the celebrated DOZZ formula) and its spectrum. Finally, we explain how it serves to “glue” together the partition functions on Riemann surfaces with boundaries. |

Effective BV quantisation of Gravity with and without boundary |

Katarzyna Rejzner (York University), Michele Schiavina (Universita degli Studi di Pavia) |

We will discuss recent developments in the effective quantisation of gravity, seen
as a field theory on manifolds with and without boundary. We will introduce techniques from
Perturbative Algebraic Quantum Field Theory as well as from the BV-BFV approach to
Lagrangian field theories, and show how they can be related. Material: Exercise sheet, Michele's slides, Katarzyna's notes. |

Random geometry in the path integral approach to quantum gravity |

Jan Ambjørn (Niels Bohr Institute) and Timothy Budd (Radboud University) |

This course will focus on the role of random geometry models in the search for a
non-perturbative description of quantum gravity. We will highlight mathematical advances in the understanding of two-dimensional toy models of quantum gravity as well as explorations
in higher-dimensional models, including (causal) dynamical triangulations. Material: Timothy's notes, Exercise sheet, Solutions, Jan's slides. |

Research talks |

Marie Albenque (IRIS) |

Slice decomposition of hypermaps. Slides. |

Giovanni Canepa (Vienna Universitaet) |

Corner Structure of Four-Dimensional General Relativity in the Coframe Formalism. Slides. |

Alicia Castro (Radboud) |

Scale-invariant random geometries from mating of trees. Slides. |