Math Papers

Preprints

  1. Geography of bilinearized Legendrian contact homology
    joint work with Damien Galant,
    preprint arXiv:1905.12037 (27 pages).

Publications

  1. S^1-equivariant symplectic homology and linearized contact homology
    joint work with Alexandru Oancea,
    International Mathematics Research Notices 2017 no 13, 3849-3937.
  2. Lagrangian cobordisms via generating families: constructions and geography
    joint work with Josh Sabloff and Lisa Traynor,
    Algebraic and Geometric Topology 15 (2015) no 4, 2439-2477.
  3. Bilinearised Legendrian contact homology and the augmentation category
    joint work with Baptiste Chantraine,
    Journal of Symplectic Geometry 12 (2014) no 3, 553-583.
  4. Contact And Symplectic Topology
    book edited with Vincent Colin and András Stipsicz,
    Bolyai Society Mathematical Studies 26, Springer, 2014.
  5. The Gysin exact sequence for S^1-equivariant symplectic homology
    joint work with Alexandru Oancea,
    Journal of Topology and Analysis 5 (2013) no. 4, 361-407.
  6. The index of Floer moduli problems for parametrized action functionals
    joint work with Alexandru Oancea,
    Geometriae Dedicata 165 (2013) no 1, 5-24.
  7. Du patinage et de l'optique à la géométrie de contact
    Bulletin de la Classe des Sciences de l'Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique (2013), no. 6.
  8. Effect of Legendrian surgery
    joint work with Tobias Ekholm and Yasha Eliashberg,
    Geometry and Topology 16 (2012), 301-389.
  9. Symplectic homology product via Legendrian surgery
    joint work with Tobias Ekholm and Yasha Eliashberg,
    Proceedings of the National Academy of Sciences 108 (2011) no 20, 8114-8121.
  10. Equivalent loads for two-dimensional distributed anisotropic piezoelectric transducers with arbitrary shapes attached to thin plate structures
    joint work with Arnaud Deraemaeker and Gilles Tondreau,
    Journal of the Acoustical Society of America 129 (2011) no 2, 681-690.
  11. Equivalent loads for flat piezoelectric transducers attached to shell structures
    joint work with Arnaud Deraemaeker and Gilles Tondreau,
    Proc ECCM 2010, Paris, France, May 2010.
  12. Lectures on symplectic and contact homology
    Proceedings of Gökova Geometry-Topology Conference (2010), 1-20.
  13. Fredholm theory and transversality for the parametrized and for the S^1-invariant symplectic action
    joint work with Alexandru Oancea,
    Journal of the European Mathematical Society 12 (2010) no 5, 1181-1229.
  14. Contact homology of left-handed stabilizations and plumbing of open books
    joint work with Otto van Koert,
    Communications in Contemporary Mathematics 12 (2010) no 2, 223-263.
  15. Towards a good definition of algebraically overtwisted
    joint work with Klaus Niederkrüger,
    Expositiones Mathematicae 28 (2010), 85-100.
  16. A survey of contact homology
    in "New Perspectives and Challenges in Symplectic Field Theory", CRM Proceedings and Lecture Notes 49 (2009), 45-72.
  17. An exact sequence for contact- and symplectic homology
    joint work with Alexandru Oancea,
    Inventiones Mathematicae 175 (2009) no 3, 611-680.
    Erratum, Inventiones Mathematicae 200 (2015) no 3, 1065-1076.
  18. Symplectic Homology, autonomous Hamiltonians, and Morse-Bott moduli spaces
    joint work with Alexandru Oancea,
    Duke Mathematical Journal 146 (2009) no 1, 71-174.
  19. A note on Reeb dynamics on the tight 3-sphere
    joint work with Kai Cieliebak and Tobias Ekholm,
    Journal of Modern Dynamics 1 (2007) No. 4, 597-613.
  20. Contact homology and homotopy groups of the space of contact structures
    Mathematical Research Letters 13 (2006) No. 1, 71-85.
  21. Homologie de contact des variétés toroïdales
    joint work with Vincent Colin,
    Geometry and Topology 9 (2005), 299-313.
  22. Coherent Orientations in Symplectic Field Theory
    joint work with Klaus Mohnke,
    Mathematische Zeitschrift 248 (2004) No. 1, 123-146.
  23. Compactness results in Symplectic Field Theory
    joint work with Yasha Eliashberg, Helmut Hofer, Kris Wysocki and Edi Zehnder,
    Geometry and Topology 7 (2003), 799-888.
  24. A Morse-Bott approach to Contact Homology
    in "Symplectic and Contact Topology : Interactions and Perspectives", Fields Institute Communications 35 (2003), 55-77.
  25. A Morse-Bott approach to contact homology
    Ph.D. Thesis, Stanford University, 2002.
  26. Odd dimensional tori are contact manifolds
    International Mathematics Research Notices 2002 (2002) No. 30, 1571-1574.
  27. Stochastic quasi-gradient based optimization algorithms for dynamic reliability applications
    joint work with Pierre-Etienne Labeau,
    Reliability Engineering and System Safety 71 (2001) No. 1, 65-79.
  28. Stochastic programming in dynamic reliability
    joint work with Pierre-Etienne Labeau,
    ESREL '99, Safety and Reliability (1999), 913-919.
  29. Can one define a preferred symplectic connection
    joint work with Michel Cahen,
    Reports on Mathematical Physics 43 (1999) No. 1/2, 35-42.
  30. A variational principle for symplectic connections
    joint work with Michel Cahen,
    Journal of Geometry and Physics 30 (1999) 233-265.

Lecture Notes

  1. Introduction to Contact Homology
  2. J-holomorphic curves and the moment map
    written jointly with Alexandru Oancea.