This page gathers some images I made for talks and summer school
lectures as well as some texts I wrote to answer questions from
colleagues about known but poorly documented results. These
texts can be less polished than papers and are provided without
any guaranties.

Why formalize mathematics?

On October 27th 2021, I gave a talk at the New Technologies in Mathematics Seminar Series in Harvard with title "Why formalize mathematics". There is a video recording and, more important, an expanded text version.

Bourbaki seminar

On March 11th 2017, I gave a Bourbaki seminar talk about Borman, Eliashberg and Murphy's work about "Flexibilité en géométrie de contact en grande dimension". There is a video recording and a text, both in French.

Habilitation

I defended my "Habilitation à Diriger les Recherches" on Monday 12th december 2016.

Images of contact structures

I made images of some examples of contact structures and isomorphisms between them. There are also examples of characteristic foliations.

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).

Convex surfaces

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.

Natural fibrations

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.

Reducible monodromies

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.

Liouville pairs on 5-dimensional Lie groups

My note on Liouville pairs explains why there are only two 5-dimensional Lie groups which have a left-invariant Liouville pair and a compact quotient. This explains why we use these groups in our weak fillability paper.

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.

PhD thesis

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.

updated on April 29 2020.