Advanced Lectures
Academic year 2023-2024
Matthieu Vilatte (CPHT, Palaiseau & Aristotle University of Thessaloniki) | Carrollian geometry in splitted formalism | 2 hrs, 4 July 2024
Carrollian spacetimes can be seen as tangent bundle whose one-dimensional fibers span the degenerate direction of the metric. Usually described in a covariant fashion, I will review and develop in these lectures a formalism adapted to this bundle structure: the splitted formalism. After reviewing the basics and the way to construct a connection, I will define the notion of Carrollian momenta and conservation equations. I shall finish with some words about isometries and charges built upon the latter and the Carrollian momenta.
Xavier Bekaert (U. Tours) | Some BMS group theory | 3 hrs, 11-13 June 2024
We will present a group-theoretical introduction to BMS algebra that circumvents its traditional bulk realisation as asymptotic symmetries. More precisely, among the potential topics which could be covered are: the abstract definition of BMS algebra, its Carrollian realisation at null infinity, its semi-direct structure, its Poincaré subalgebras, its unitary representations.
Marios Petropoulos (CPHT, Palaiseau) | Continuous media on Newton-Cartan spacetimes | 4 hrs, 24-27 May 2024
The content and plan of these lectures is as follows:
1) Reminder of basics on “continuous media equations”.
2) Following the paradigm of infinite-c limit, description of Newton-Cartan spacetimes with emphasis on the action of Galilean boosts on the tangent and cotangent spaces.
3) Description of the connections with torsion in the case of strong Newton-Cartan structures with emphasis on the split-time-and-space paradigm.
4) Galilean hydrodynamics as the limit of Lorentzian fluid equations, contact with the connection previously introduced.
5) Equations from variational principle, back to the Galilean boosts, back to a generalized connection with further degrees of freedom.