Speakers
 JeanPierre Bourguignon, IHÉS (14 lectures) and
 David Langlois, CNRS (6 lectures)
Date
31 July – 4 August 2023
Location
DIAS Auditorium, University of Southern Denmark, Campusvej 55, DK 5230 Odense, Denmark
Registration deadline
To apply for financial support: 16 July 2023
Please register in the form below.
Aimed audience
Master and PhD students in mathematics and mathematical physics.
Organizer
Centre Director Jørgen Ellegaard Andersen, Centre for Quantum Mathematics
Contact
Centre Administrator, Jane Jamshidi, jaja@sdu.dk
Geometric variational problems (shortest paths, minimal surfaces, harmonic maps, YangMills fields, CherSimons functional, …) have a long history going back to the EulerLagrange 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.
Monday 31July
09:45‐10:30 
The Setting (by JeanPierre Bourguignon)

10:45‐11:30 
Geometric Objects (by JeanPierre Bourguignon)

14:15‐15:00 
Revisiting the Prototypical Calculus of Variations (by JeanPierre Bourguignon)

15:15‐16:00 
Covariant derivatives (by JeanPierre Bourguignon)

Tuesday 1 August
09:45‐10:30 
A Quick Panorama of Geometric Functionals (by JeanPierre Bourguignon)

10:45‐11:30 
The Einstein Equations (Lecture by JeanPierre Bourguignon)

14:15‐15:00 
General Relativity and its main physical consequences 1/2 (by David Langlois) 
15:15‐16:00 
General Relativity and its main physical consequences 2/2 (by David Langlois) 
Wednesday 2 August
09:45‐10:30 
A Panorama of Critical Objects (by JeanPierre Bourguignon)

10:45‐11:30 
Groups of symmetries (by JeanPierre Bourguignon)

14:15‐15:00 
Modified gravity in cosmology: dark energy 1/2 (by David Langlois) 
15:15‐16:00 
Modified gravity in cosmology: dark energy 2/2 (by David Langlois) 
Thursday 3 August
09:45‐10:30 
Modified Lagrangians (by JeanPierre Bourguignon)

10:45‐11:30 
Testing gravity beyond General Relativity 1/2 (by David Langlois) 
14:15‐15:00 
Testing gravity beyond General Relativity 2/2 (by David Langlois) 
15:15‐16:00 
Conservation Laws (by JeanPierre Bourguignon)

Friday 4 August
09:45‐10:30 
Harmonic and Holomorphic Maps (by JeanPierre Bourguignon)

10:45‐11:30 
Selfdual YangMills Fields (by JeanPierre Bourguignon)

14:15‐15:00 
The Prescribed Curvature Problem (by JeanPierre Bourguignon)

15:15‐16:00 
Epilogue: the Hamiltonian Side (by JeanPierre Bourguignon)

Admittance
You have to be admitted to participate in the event. If we cannot verify your affiliation and that you will scientifically benefit from the event, you will be asked to supply documentation.
Included
There is no participant fee.
Included in the event is MondayFriday lunch + 2 x coffee/tea (mornings/afternoons).
Financial support
You can apply for support for the accommodation. Apply via the registration form below. We will prioritize junior researchers without other means of funding. We are unfortunately not able to offer support for the travel expenses.
Accommodation
We recommend the affordable Hotel Cabinn, which is located right next to the train station (SDU agreement is DKK 412 per night + breakfast. This price may increase by 13%).
Alternatively there are many Airbnb options in Odense.
Directions
To Odense: You can fly to Copenhagen Airport (CPH) or Billund Airport (BLL) both have 1½ to 2 hours travel time to Odense. From CPH there is a train option directly from the airport to Odense and from BLL all travel to Odense is with min. 1 transfer (bus + train). You can find the connections at: https://rejseplanen.dk/
To SDU: from Odense train station (20 min. by light rail ‘Letbane’ / 5 km): the interval between the rides is 7,5 min. during rush hours and 15 min. the rest of the day. Tickets can be purchased at the ticket automat at Odense train station & online https://webshop.fynbus.dk/ (choose from “Odense Banegaard” to “SDU”).
At SDU: download the app 'SDU Maps' or search SDU Maps online and enter 'DIAS Auditorium' or 'V24501a0'. After admittance to the event you will also receive a pdfversion of the SDU map via email.