{"id":1125,"date":"2024-05-28T12:19:44","date_gmt":"2024-05-28T10:19:44","guid":{"rendered":"https:\/\/web.umons.ac.be\/pucg\/?page_id=1125"},"modified":"2025-03-14T18:39:42","modified_gmt":"2025-03-14T17:39:42","slug":"advanced-lectures","status":"publish","type":"page","link":"https:\/\/web.umons.ac.be\/pucg\/en\/research-activities\/seminars-workshops\/advanced-lectures\/","title":{"rendered":"Advanced Lectures"},"content":{"rendered":"
Academic year 2024-2025<\/h5>\n

 <\/p>\n

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Felipe Figueroa<\/strong> (UMONS) |\u00a0Introduction to the S-matrix bootstrap program<\/strong><\/em> | 4 hrs, 4-7 March 2025<\/p>\n

The S-matrix bootstrap program is an approach whose aim is to understand the space of scattering amplitudes consistent with analyticity, causality and crossing symmetry, which form a\u00a0set of basic principles that physical theories are assumed to satisfy.<\/p>\n

In this short series of lectures I will review the basic ideas of the program, giving a short introduction to S-matrix theory as well as motivating the requirement that physical S-matrices satisfy this set of axioms. \u00a0I will derive the implications of analyticity, causality and crossing symmetry on scattering amplitudes and show how they can be recasted as a set of constraints that amplitudes must satisfy. I will finish by providing some examples of recent implementations of these ideas in the context of QFT in d=2 and d=4.<\/p>\n

 <\/p>\n

Academic year 2023-2024<\/h5>\n

 <\/p>\n

\n

Matthieu Vilatte<\/strong> (CPHT, Palaiseau & Aristotle University of Thessaloniki) | Carrollian geometry in splitted formalism<\/em><\/strong> | 2 hrs, 4 July 2024<\/p>\n

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.<\/p>\n

 <\/p>\n

\n

Xavier Bekaert<\/strong> (U. Tours) | Some BMS group theory<\/em><\/strong> | 3 hrs, 11-13 June 2024<\/p>\n

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 Poincar\u00e9 subalgebras, its unitary representations.<\/p>\n

[Slides of part I]<\/a><\/p>\n

 <\/p>\n

\n

Marios Petropoulos<\/strong> (CPHT, Palaiseau) | Continuous media on Newton-Cartan spacetimes<\/strong><\/em> | 4 hrs, 24-27 May 2024<\/p>\n

The content and plan of these lectures is as follows:<\/p>\n

1) Reminder of basics on \u00ab\u00a0continuous media equations\u00a0\u00bb.<\/p>\n

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.<\/p>\n

3) Description of the connections with torsion in the case of strong Newton-Cartan structures with emphasis on the split-time-and-space paradigm.<\/p>\n

4) Galilean hydrodynamics as the limit of Lorentzian fluid equations, contact with the connection previously introduced.<\/p>\n

5) Equations from variational principle, back to the Galilean boosts, back to a generalized connection with further degrees of freedom.<\/p>\n

[Lecture notes]<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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