Summaries, lecture notes
and advised reading

Hopf algebras and quantum groups Theory of black holes BRST Algebraic geometry and K-theory Representations of the Poincaré group Topology of fiber bundles and instantons The latest version of the complete lecture notes is available here.

• Theory of black holes  (G. Compère):   
• These lectures present the mathematical tools necessary to demonstrate
  the zero, first and second laws of black hole mechanics.
  The lectures are self-contained but assume a basic knowledge
  of general relativity.
  
• Plan of the lecture:
  1. Event horizons
  2. Equilibrium states
  3. Conservations laws
  4. Quasi-equilibrium states
  
• Lecture notes: notes (pdf)
• Advised references:
  P. K. Townsend, "Black holes", gr-qc/9707012,
  R. M. Wald, "The Thermodynamics of black holes", Living Rev. Rel. 4 (2001) 6, [gr-qc/9912119].

• BRST  (S. Leclercq, S. Cnockaert, N. Bouatta, C. Maccaferri):   
• Plan of the lecture:
  1. Introduction to the BRST antifield formalism
  2. Applications of the antifield formalism
  3.
  4. Introduction to open string field theory
• Lecture notes: partII (pdf), partIV (pdf)
• Advised references:
  For parts 1. and 2.:
  -THE reference: M.Henneaux, C.Teitelboim, "Quantization of gauge systems";
    Princeton, USA: Univ.Pr. (1992).
  Some reviews:
  -J.Gomis, J.Paris and S.Samuel, "Antibracket, antifields and gauge theory quantization";
   Phys.Rept.259:1-145,1995; [hep-th/9412228].
  -A.Fuster, M. Henneaux, A.Maas, "BRST quantization: A short review.";
   Int.J.Geom.Meth.Mod.Phys.2:939-964,2005; [hep-th/0506098].
  For part 4.:
  - K. Ohmori, "A review of tachyon condensation in open string field theories",  [hep-th/0102085].
  - C. B. Thorn, ``String Field Theory,'' Phys. Rept. 175 (1989) 1.
  - W. Taylor and B. Zwiebach, ``D-branes, tachyons, and string field theory,'' [hep-th/0311017].
  - A. Sen, ``Tachyon dynamics in open string theory,''
   Int. J. Mod. Phys. A 20 (2005) 5513  [arXiv:hep-th/0410103].
  

• Algebraic geometry and K-theory (J. Evslin, W. Jiang):   
• Plan of the lecture:
  
• Lecture notes: notes (pdf)
• Advised references:
  
  

• Representations of the Poincaré group (X. Bekaert, N. Boulanger):   
• Plan of the lecture:
  1. Group-theoretical preliminaries
  2. Elementary particles as irreducible representations of the isometry group
  3. Classification of the unitary representations
  4. Tensorial irreducible representations and Young diagrams
  5. Relativistic wave equations
  
• Lecture notes: 
• Advised references:
  

• Topology of fiber bundles and instantons (A. Collinucci, A. Wijns):   
• Plan of the lecture:
  
  
• Lecture notes: 
• Advised references: