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
France

Email: cyril.falcon@math.u-psud.fr
Office: 2R21



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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.

Preprints

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

Conferences and seminars

Teaching

  • 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)

Miscellaneous

You can also find me on Mathematics Stack Exchange.


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