Research interests

I investigate contact rigidity aspects of isotopies through closed Legendrian submanifolds in contact manifolds by studying the algebraic structure of Legendrian submanifolds invariants constructed from generating families. From a general perspective, I am also interested in the categorical correspondence between these invariants and the ones built from pseudo-holomorphic curves and constructible sheaves.

Key words. Legendrian submanifolds, Contact rigidity, Generating families, Moduli spaces analysis.

I am working on a conjecture made by M. B. Henry and D. Rutherford in 2013 regarding how to compute the differential for generating family homology of Legendrian submanifolds from their front projections by counting ”gradient staircases” flow lines. In my thesis, I addressed this question by studying an adiabatic relaxation process for gradient flows of difference functions and developping an appropriate compactness-gluing strategy. I showed that the trajectories of the associated slow-fast dynamical systems "accumulate" on chains of gradient staircases.

Research papers

1. Statistical validation method for robust data fusion with an INS
   With Thomas Brunner and Jean-Philippe Michel.
   (in preparation).
2. A Floer-Gromov type compactness result for moduli spaces in generating family theory of Legendrian submanifolds
   (in preparation).
3. General planar bias in identifying most efficient paths in non-Euclidean geometries
   With Charlotte Barot and Véronique Izard.
   (to be submitted).
4. Generating family homologies of Legendrian submanifolds and moduli spaces of gradient staircases
   Doctoral thesis, Université Paris-Saclay, defended on January 25th, 2023.
   Supervisor: Professor Frédéric Bourgeois.
   President: Professor Claude Viterbo [Defence report (in French)].
   Referees and examinators: Professor Alexandru Oancea [Report (in French)] and Professor Lisa Traynor [Report].
   Examinators: Baptiste Chantraine, Ph.D. and Professor Urs Frauenfelder.
   [Dissertation and slides]

Research talks

• Generating family homology of Legendrian submanifolds and moduli spaces of gradient staircases
  Symplectix, IHP, Paris (France), December 2nd, 2022.
  [Handwritten notes (in French)]
• Generating family homology of Legendrian submanifolds and moduli spaces of gradient staircases
  CoSy ANR launch meeting, IMJ-PRG, Paris (France), February 4th, 2022.
  [Handwritten notes (in French)]
• A compactness result in generating family theory
  Geometry, Topology and Dynamics seminar, LMO, Orsay (France), September 10th, 2020.
  [Slides (in French)]

If you are looking for the informal talks I gave, please visit my Teaching and outreach page.

Research events attended

Recurring events

• Geometry, Topology and Dynamics seminar
  LMO, Orsay (France), weekly from September 2018 to June 2022.
• Symplectix working group
  IHP, Paris (France), monthly from September 2018-June 2022.
• Nantes-Orsay seminar on Symplectic and Contact Geometry
  LMJL, Nantes (France) and LMO, Orsay (France), five yearly from September 2018 to June 2022.
• Workshop on Symplectic Geometry, Contact Geometry, and Interactions (CAST)
  CAST XIV, Universiteit Antwerpen, Antwerpen (Belgium), February 11-13, 2020.
  CAST XIII, Humboldt-Universität, Berlin (Allemagne), March 7-9, 2019.

One-time events

• Advances in Symplectic Topology
  Online event, May 17-21, 2021.
• From Hamiltonian Dynamics to Symplectic Topology
  Online event, April 26-30, 2021.
• Research school on Symplectic and Contact Topology
  ÉNS, Paris (France), April 19-23, 2021.
• Lebesgue doctoral meetings (in French)
  Université de Nantes, Nantes (France), October 28-30, 2019.
• From celestial Mechanics to Reeb Flows
  104th encounter between Mathematicians and Theoretical Physicists
  IRMA, Strasbourg (France), September 19-20, 2019.
• Differential Topology and mathematics of today, a conference in honor of Jean Cerf
  LMO, Orsay (France), June 11-13, 2018.

Other research-related writings

• Homological invariants of Legendrian submanifolds obtained from generating families
  Introduction to my research field (2018).
  [PDF file (in French)]
• Geography of the generating family homology
  Master's thesis (2018)
  Under the supervision of Professor Frédéric Bourgeois.
  [PDF file (in French)]

If you are looking for my other mathematical writings, please visit my Miscellaneous page.