A working seminar on the geometry of supergravity

This is the website for a working seminar on an approach to the classification problem of supersymmetric (eleven-dimensional) supergravity backgrounds based on their Killing superalgebras.

Unless otherwise stated, the seminars will take place on Thursdays at 9-11am (breakfast not included) in JCMB 6206.

Schedule of seminars

1. Thursday, 1 October 2015
   José Figueroa-O'Farrill
   Eleven-dimensional supergravity
   Poincaré superalgebra, eleven-dimensional supergravity, supersymmetric backgrounds
2. Thursday, 8 October 2015
   José Figueroa-O'Farrill
   The Killing superalgebra of a supersymmetric background
   The Killing superalgebra, the homogeneity theorem
3. Thursday, 15 October 2015
   Andrea Santi
   Introduction to G-structures
   Basic definitions and examples, symmetries of integrable model, automorphims of absolute parallelism.
4. Thursday, 22 October 2015
   Andrea Santi
   Prolongations of G-structures
   Prolongations, automorphism groups.
5. Thursday, 29 October 2015
   Andrea Santi
   The integrability problem for G-structures
   Obstructions to integrability given by generalized curvatures
6. Thursday, 5 November 2015
   Andrea Santi
   Eleven-dimensional supergravity (revisited)
   Superspace approach, Howe's theorem
7. Thursday, 12 November 2015
   Andrea Santi
   Tanaka structures
   Prolongations of non-holonomic G-structures, automorphism group
8. Thursday, 19 November 2015
   Andrea Santi
   The gap phenomenon
   Lacunae given by the submaximal possible dimension of the automorphism group
9. Thursday, 26 November 2015
   TBA
   TBA

References

• Supersymmetry and homogeneity in M-theory backgrounds
  José Figueroa-O'Farrill, Patrick Meessen and Simon Philip
• The homogeneity theorem for supergravity backgrounds
  José Figueroa-O'Farrill and Noel Hustler
• Transformation Groups in Differential Geometry (PDF)
  Shōshichi Kobayashi
• Introduzione ai Gruppi di Transformazioni (PDF, Italian)
  Fabio Podestà and Andrea Spiro
• Geometry associated with semisimple flat homogeneous spaces
  Takushiro Ochiai
• The integrability problem for G-Structures
  Victor Guillemin
• A generalized integrability problem for G-structures
  Andrea Santi
• Prolongations of Tanaka structures and CR structures (PDF)
  Dmitri Alekseevsky and Andrea Spiro
• Tanaka structures (non-holonomic G-structures) and Cartan connections
  Dmitri Alekseevsky and Liana David
• On automorphism groups of some types of generic distributions
  Andreas Čap and Katharina Neusser
• The gap phenomenon in parabolic geometries
  Boris Kruglikov and Dennis The
• Generalized Spencer cohomology and filtered deformations of $\mathbb{Z}$-graded Lie superalgebras
  Shun-Jen Cheng and Victor Kac
• Weyl superspace
  Paul Howe
• Super-Poincaré algebras, space-time and supergravities (I)
  Andrea Santi and Andrea Spiro
• Super-Poincaré algebras, space-time and supergravities (II)
  Andrea Santi and Andrea Spiro