Professeurs

Lalonde, François

Professeur titulaire

Doctorat d'État, Paris-Sud (Orsay) 1985

Contact :

  • Téléphone 514-343-6707 Pav. André-Aisenstadt \ bur. AA-6143
Département de mathématiques et de statistique

Intérêts de recherche


Summary of Vitae in English

CV in English

Mes travaux les plus récents se rapportent à la topologie symplectique et aux systèmes hamiltoniens ainsi qu'à une théorie de Floer universelle des lagrangiennes, sujet qui a fait l'objet d'un intense développement depuis une vingtaine d'années. La topologie (ou géométrie) symplectique est l'étude mathématique des espaces courbes, de dimension paire arbitraire, munis d'une forme symplectique, analogue anti-symétrique d'une métrique riemannienne, qui donne à ces espaces la structure qu'il faut pour donner un sens aux lois de la physique aussi bien qu'aux procédés de quantification (passage du classique au quantique). Ce sujet est le versant mathématique de ce que les physiciens appellent la théorie des super-cordes. Son développement a attiré l'attention des physiciens (Witten, Vafa) aussi bien que celle des mathématiciens (Gromov, Donaldson), et les méthodes employées ont suivi une évolution rapide au cours des dernières années. La plupart de mes travaux porte sur les aspects dits ``hard'' de la topologie symplectique et des systèmes hamiltoniens, en se servant de techniques topologiques, géométriques et analytiques, en particulier des méthodes d'équations aux dérivées partielles elliptiques et de la cohomologie quantique. Ces méthodes sont fondées sur l'étude du comportement de différents espaces de modules de courbes pseudoholomorphes, qui sont solutions d'équations de Cauchy-Riemann généralisées associées à une structure presque complexe.


Articles choisis

  • , The Hofer Geometry of Surfaces, preprint, (2012)
  • , Homological Lagrangian Monodromy, 15 1617-1650 (2011) Geometry and Topology
  • , g-areas and commutator length, preprint, (2011)
  • , Minimality in the Hofer geometry of Lagrangians, preprint, (2011)
  • , Non-splitting of certain groups of Hamiltonian diffeomorphisms, preprint, (2011)
  • , A relative Seidel morphism and the Albers map, 362 1135-1168 (2009) Trans. Amer. Math. Soc.
  • , The homotopy type of the space of symplectic balls in rational ruled 4-manifolds, 13 1177-1227 (2009) Geometry and Topology
  • , The full homotopy type of symplectic balls in S^2 x S^2 above the critical value, preprint arXiv:math/0406129, (2008) 23 pages ,
  • , Anti-symplectic involutions and Maslov indices, preprint, (2008) 18 pages ,
  • , The topology of the space of symplectic balls in S^2 x S^2, 345 639-642 (2007) C. R. Acad. Sci. Paris, Ser. I
  • , Lagrangian submanifolds: from the local model to the cluster complex, 456-477 (2006) Proceedings of the International Congress of Mathematicians
  • , Cluster Homology, (2006) 56 pages , ArXiv Math.SG/0508345
  • , Cluster homology: an overview of the construction and results, 12 1-12 (2006) ERA-AMS
  • , A field theory for symplectic fibrations over surfaces with applications, 8 1189-1226 (2004) Geometry and Topology
  • , The topology of the space of symplectic balls in rational 4-manifolds, 122 347-397 (2004) Duke Mathematical Journal
  • , Length minimising paths for symplectically aspherical manifolds, 53 1503-1526 (2003) Ann. Inst. Fourier
  • , Symplectic structures on fiber bundles, 42 309-347 (2003) Topology
  • , Groupes d'automorphismes et plongements symplectiques de boules dans les variétés rationelles, 335 931-934 (2002) C.R. Acad. Sci. Paris, Ser. I
  • , Cohomological properties of ruled symplectic structures on manifolds, Mirror Symmetry IV, 33 79- (2002) AMS/IP Studies in Advanced Mathematics
  • , Holomorphic cylinders with Lagrangian boundaries and Hamiltonian dynamics, 102 485 (2000) Duke Mathematical Journal
  • , Stabilisation of symplectic inequalities and applications, 196 63-72 (1999) Amer. Math. Soc. Translations, Series 2
  • , Topological rigidity of Hamiltonian loops and quantum homology, 135 369-385 (1999) Inventiones Mathematicae
  • , On the Flux conjectures, 15 69-86 (1998) CRM Proceedings and Lecture Notes, American Mathematical Society
  • , J-curves and symplectic invariants, in:, (1997) J. Hurtubise and F. Lalonde (eds), Proceedings of the NATO Summer Advanced Institute (SMS) on Gauge Theory and Symplectic Geometry Université de Montréal 1995, Kluwer Academic Publishers, Dordrecht
  • , New trends in symplectic geometry, 19 (2) 33-50 (1997) invited survey in the new series of C.R. Math. Rep. Acad. Sci. Canada
  • , Energy and capacities in symplectic topology, in: , 2 328-374 (1997) W.H. Kazez (ed.), Geometric Topology, Studies in Advanced Mathematics, American Mamthematical Society and International Press
  • , Positive paths in the linear symplectic group, 1-20 (1997) The Arnold-Gelfand seminar, Birkhauser
  • , Symplectic diffeomorphisms as isometries of Hofer's norm, 36 711-728 (1997) Topology
  • , J-holomorphic curves and the classification of rational and ruled symplectic 4-manifolds, in:, 1-40 (1996) C.B. Thomas (ed.), Symplectic and Contact Geometry, Proceedings of the Newton Institute Special Year on Symplectic Geometry, Cambridge University Press
  • , The classification of ruled symplectic 4-manifolds, 3 769-778 (1996) Mathematical Research Letters
  • , The geometry of symplectic energy, 141 349-371 (1995) Annals of Mathematics
  • , Hofer's $L^{\infty}$-geometry: energy and stability of Hamiltonian flows part II, 122 35-69 (1995) Inventiones Mathematicae
  • , Hofer's $L^{\infty}$-geometry: energy and stability of Hamiltonian flows part I, 122 1-34 (1995) Inventiones Mathematicae
  • , Local Non-Squeezing Theorems and Stability, 364 (1995) Geometric and Functional Analalysis 5 (Special volume in the honour of M. Gromov)
  • , Symplectic rigidity: Lagrangian submanifolds, in: , 117 271-322 (1994) M. Audin and J. Lafontaine (eds.), Holomorphic Curves in Symplectic Geometry, Progress in Mathematics
  • , Isotopy of symplectic balls, Gromov's radius, and the structure of irrational ruled symplectic 4-manifolds, 300 273-296 (1994) Mathematische Annalen

Monographies et proceedings

  • , New Perspectives and Challenges in Symplectic Field Theory, 49, 342 (2009) The CRM Proceedings and Lecture Notes
  • , Morse theoretical methods in symplectic topology and non-linear analysis, Kluwer Academic Publishers, Dordrecht (2005) Proceedings of the NATO Advanced Study Institute (Montréal, 2004),
  • , Symplectic and Contact Topology: Interactions and Perspectives, Fields Institute Communications 35, AMS (2003) Proceedings of the workshop on ''Symplectic topology and higher dimensional Gauge invariants'' (held at the Fields Institute in March-April 2001),
  • , Proceedings of the CRM Workshop on Geometry, Topology and Dynamics (Montréal 1995), 15, AMS (1998) CRM Proceedings and Lecture Notes
  • , Gauge Theory and Symplectic Geometry, Kluwer Academic Publishers, Dordrecht (1997) Proceedings of the NATO Summer Advanced Institute on Gauge Theory and Symplectic Geometry (Montréal 1995),

Postdoctorants

Étudiants dirigés