Publications

2012

• Geometry of representation spaces in SU(2)
  
  • Marche Julien
  IRMA - Lectures in Mathematics and Theoretical Physics, EMS, 2012, 12, pp.333-370. These notes of a course given at IRMA in April 2009 cover some aspects of the representation theory of fundamental groups of manifolds of dimension at most 3 in compact Lie groups, mainly $\su$. We give detailed examples, develop the techniques of twisted cohomology and gauge theory. We review Chern-Simons theory and describe an integrable system for the representation space of a surface. Finally, we explain some basic ideas on geometric quantization. We apply them to the case of representation spaces by computing Bohr-Sommerfeld orbits with metaplectic correction.
• Semiclassical and spectral analysis of oceanic waves
  
  • Cheverry Christophe
  • Gallagher Isabelle
  • Paul Thierry
  • Saint-Raymond Laure
  Duke Mathematical Journal, Duke University Press, 2012, 161 (5), pp.845-892. In this work we prove that the shallow water flow, subject to strong wind forcing and linearized around an adequate stationary profile, develops for large times closed trajectories due to the propagation of Rossby waves, while Poincaré waves are shown to disperse. The methods used in this paper involve semi-classical analysis and dynamical systems for the study of Rossby waves, while some refined spectral analysis is required for the study of Poincaré waves, due to the large time scale involved which is of diffractive type.