I defended my "Habilitation à Diriger les Recherches" on Monday 12th december 2016.
Introduction to contact structures in dimension 3 and symplectic fillings
During the precourse of the SFT 6 workshop, I lectured on various topological aspects of contact geometry in dimension 3 including definitions and examples of symplectic fillings, Legendrian surgery and flexibility of overtwisted contact structures. There are lecture notes (in pdf).
During the summer school Symplectic and contact topology in Nantes I wrote lecture notes on Topological methods in 3-dimensional contact geometry (pdf file). There is also a web page page on convex surfaces.
My paper with Emmanuel Giroux about contact transformations uses some folklore results which are explained in some more details in my expository note on natural fibrations in contact topology. This includes the natural statement of "Gray's theorem with parameters" and "isotopies of surfaces in a contact 3-manifold with constant characteristic foliation come from ambient contact isotopies".
The Giroux correspondance
My page on the Giroux correspondance is a series of pictures with short explanation explaining the relation between open books and contact structures.
Open books for contact element bundles and the support genus question
My remarks on the support genus is a note I wrote to explain why the canonical contact structure on the unit tangent bundle of a hyperbolic surface is supported by a genus one open book and why this result was mostly known since 1917.
My note on reducible monodromies explains an obvious but poorly undocumented (as far as I know) result. Tori which are transverse to pages of an open book correspond to curves which are preserved by the monodromy and they are isotopic to prelagrangian tori. In particular a Dehn twist along such a torus does not modify the contact structure up to isotopy.
A cobordism between Giroux torsion and overtwisted disks
As a side effect of our weak fillability paper, there is now a very short elementary proof of the Gay-Wendl theorem: any closed contact 3-manifold with positive Giroux torsion is the concave end of a weak symplectic cobordism whose convex end is overtwisted.
Loose Legendrian submanifolds
My page on Murphy's flexibility theorem is a series of animations introducing the Legendrian isotopy problem in higher dimension.
Elementary theory of line bundles
My notes on line bundles were written for a summer school on Donaldson approximately holomorphic techniques. It explains the Euler class of a complex line bundle from a point of view suitable for the discussion of Donaldson technique. In particular it contains an elementary and self-contained construction of a line bundle starting from a closed 2-form with integral cohomology class.
My PhD thesis deals with interactions between Riemannian geometry and contact topology. It also contains detailed and illustrated explanations about Giroux's theory of tight contact structures on toric annuli and related closed 3-manifolds.