Masterclass – Geometric Variational Problems (General Relativity)
Αγαπητοί/ές φοιτητές/τριες,
Δείτε πιο κάτω την ανακοινωση για το συγκεκριμένο Masterclass με δυνατότητα χρηματοδότησης.
Π. Μπατακίδης
QM Masterclass
Geometric Variational Problems: Diversity and Common Patterns
with a Special Emphasis on General Relativity
Speakers Jean-Pierre BOURGUIGNON (IHES) & David LANGLOIS (APC, CNRS – Univ. Paris Cité)
Time 31 July-4 August 2023
Length 20 lectures
Location University of Southern Denmark, Odense, Denmark
Website (registration by June 18 – with application for funding / July 16 without funding): https://www.sdu.dk/en/forskning/qm/events/masterclasses/qm-masterclass-gvp
Topic
Geometric variational problems (shortest paths, minimal surfaces, harmonic maps, Yang-Mills fields, Chern-Simons functional, …) have a long history going back to the Euler-Lagrange equation of the Calculus of Variations. They pose mathematical challenges and are also essential tools to provide key field equations in Mechanics and Physics. The setting of bundles and connections, finally formalised in the mid 20th century, provides the appropriate context to deal with these problems in a systematic way, establishing curvature as a central object to be taken into consideration. The interaction of these problems with theoretical physics has grown substantially in the second part of the 20th century because of the very successful trend to develop a geometric approach to a number of theories through a variety of Lagrangians. It is quite remarkable that this trend was introduced for the first time in the theory of General Relativity, making this theory an example especially worthy of special consideration in the context of this set of lectures.
This led to the idea that, to complement this somewhat comprehensive panorama of variational problems, a good way to get useful illustrations of the power of these geometric approaches was to look in some depth at the theory of General Relativity and some other models of gravity. The lectures on this topic will take into consideration Lagrangians of modified gravity and mention some observational tests, subjects which have received renewed attention recently.
Familiarity with objects of Differential Geometry will be assumed but they will be reviewed systematically. In the same way, some basic knowledge of the setting of Mechanics and Theoretical Physics will be useful to follow the articulation with modern mathematical considerations.
The Masterclass is aimed at Master and PhD students in mathematics and mathematical physics but all interested in the topic are welcome.