Cyril Falcon

Doctoral student (second year), advisor Prof. Frédéric Bourgeois
Team of Topology and Dynamics

Curriculum vitæ

Laboratoire de Mathématiques d'Orsay
Université Paris-Sud
Bâtiment 307
91405 Orsay Cedex

Office: 2R21

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Version française

Research interests

My work is in symplectic and contact topology, my main questions concerns the two following axes:
  • Structure of the algebraic invariants of Legendrian submanifolds,
  • Applications of generating families (Morse-Bott-Cerf theory) to contact topology.
My current research aims to develop a straightforward and efficient way to compute generating family homology of Legendrian submanifolds in 1-jet bundles. This work could finally allow to relate linearized Legendrian contact homology to generating family homology.

My strategy is inspired by a conjecture by M. Henry and D. Rutherford and is similar to the one of F. Bourgeois and A. Oancea for the construction of the Floer homology of a time-independent Hamiltonian. However, the compactness result requires now a much more involved geometric analysis using ideas of T. Elkhom to compute Legendrian contact homology in terms of Morse flow trees.


  • C. Falcon, A compactness result in generating family theory, in preparation.

Conferences and seminars


  • 2019-2020, first year of Bachelor of Science (linear algebra tutorials), first year of Polytech engineering course (refresher tutorials).
  • 2018-2019, first year of DUT Computer Science studies (discrete mathematics and linear algebra tutorials).

Popularization of mathematics

Dissertations (in French)


You can also find me on Mathematics Stack Exchange.

Département de Mathématiques
, Université Paris-Sud, Bât. 307, F-91405 Orsay Cedex, France