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Lalonde, François

Vcard

Professeur titulaire

Faculté des arts et des sciences - Département de mathématiques et de statistique

André-Aisenstadt Local 6143

514 343-6707

Courriels

Affiliations

  • Membre Centre de recherches mathématiques
  • Titulaire Chaire de recherche du Canada en géométrie différentielle et topologie
  • Membre CRM — Centre de recherches mathématiques

Cours donnés

  • MAT6330 A - Géométrie différentielle

Expertise

Chaire de recherche du Canada

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 s 19est d'abord fait par les mathématiciens (Gromov, Donaldson, 26) et les physiciens (Witten, Vafa,...) et les méthodes employées ont littéralement explosé 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.

 

Projets de recherche Tout déplier Tout replier

Fundamental and Statistical Symplectic Topology CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2018 - 2024

FGR-CRSNG_2017-2018 CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2017 - 2018

CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2015 - 2023

CANADA RESEARCH CHAIR IN DIFFERENTIAL GEOMETRY AND TOPOLOGY SPIIE/Secrétariat des programmes interorganismes à l’intention des établissements / 2015 - 2022

COURBES J-HOLOMORPHES ET RIGIDITE EN TOPOLOGIE SYMPLECTIQUE ET EN PHYSIQUE-MATHEMATIQUE FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2013 - 2017

CENTRE DE RECHERCHE MATHÉMATIQUE FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2013 - 2015

DEMANDE DE STAGE INTERNATIONAL POUR LAURENT DELISLE FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2012 - 2014

DEMANDE DE STAGE INTERNATIONAL POUR MUATH KARAKI FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2012 - 2014

DEMANDE DE STAGE INTERNATIONAL POUR VIRGILE DUCET FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2012 - 2014

DEMANDE DE STAGE INTERNATIONAL POUR XAVIER GLOROT FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2012 - 2014

QUANTUM TOPOLOGY OF LAGRANGIAN SUBMANIFOLDS CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2011 - 2017

QUANTUM TOPOLOGY OF LAGRANGIAN SUBMANIFOLDS / 2011 - 2015

CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2008 - 2016

CANADA RESEARCH CHAIR IN DIFFERENTIAL GEOMETRY AND TOPOLOGY SPIIE/Secrétariat des programmes interorganismes à l’intention des établissements / 2008 - 2015

Publications choisies Tout déplier Tout replier

An example concerning Hamiltonian groups of self product II

Hu, Shengda et Lalonde, François, An example concerning Hamiltonian groups of self product II 14, 234--247 (2013), , Afr. Diaspora J. Math.

An example concerning Hamiltonian groups of self product I

Hu, Shengda et Lalonde, François, An example concerning Hamiltonian groups of self product I 14, 227--233 (2013), , Afr. Diaspora J. Math.

The $g$-areas and the commutator length

Lalonde, François et Teleman, Andrei, The $g$-areas and the commutator length 24, 1350057, (2013), , Internat. J. Math.

The Hofer Geometry of Surfaces, preprint

F. Lalonde and Y. Savelyev, The Hofer Geometry of Surfaces, preprint , (2012), ,

Homological Lagrangian Monodromy

S. Hu, F. Lalonde and R. Leclercq, Homological Lagrangian Monodromy 15, 1617-1650 (2011), , Geometry and Topology

g-areas and commutator length, preprint

F. Lalonde and A. Teleman, g-areas and commutator length, preprint , (2011), ,

Minimality in the Hofer geometry of Lagrangians, preprint

E. Kerman and F. Lalonde, Minimality in the Hofer geometry of Lagrangians, preprint , (2011), ,

Non-splitting of certain groups of Hamiltonian diffeomorphisms, preprint

S. Hu and F. Lalonde, Non-splitting of certain groups of Hamiltonian diffeomorphisms, preprint , (2011), ,

New Perspectives and Challenges in Symplectic Field Theory

M. Abreu, F. Lalonde, L.Polterovich (eds), New Perspectives and Challenges in Symplectic Field Theory 49,, 342 (2009), , The CRM Proceedings and Lecture Notes

A relative Seidel morphism and the Albers map

S. Hu and F. Lalonde, 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

S. Anjos, F. Lalonde and M. Pinsonnault, 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 $S^2 \times S^2$ above the critical value, preprint arXiv:math/0406129

S. Anjos and F. Lalonde, The full homotopy type of symplectic balls in $S^2 \times S^2$ above the critical value, preprint arXiv:math/0406129 , (2008), 23 pages ,

Anti-symplectic involutions and Maslov indices, preprint

S. Hu and F. Lalonde, Anti-symplectic involutions and Maslov indices, preprint , (2008), 18 pages ,

The topology of the space of symplectic balls in $S^2 \times S^2$

S. Anjos and F. Lalonde, The topology of the space of symplectic balls in $S^2 \times S^2$ 345, 639-642 (2007), , C. R. Acad. Sci. Paris, Ser. I

Lagrangian submanifolds: from the local model to the cluster complex

F. Lalonde, Lagrangian submanifolds: from the local model to the cluster complex , 456-477 (2006), , Proceedings of the International Congress of Mathematicians

Cluster homology: an overview of the construction and results

O. Cornea and F. Lalonde, Cluster homology: an overview of the construction and results 12, 1-12 (2006), , ERA-AMS

Cluster Homology

O. Cornea and F. Lalonde, Cluster Homology , (2006), 56 pages , ArXiv Math.SG/0508345

Morse theoretical methods in symplectic topology and non-linear analysis

P. Biran, O. Cornea and F. Lalonde (eds), Morse theoretical methods in symplectic topology and non-linear analysis Kluwer Academic Publishers,, Dordrecht (2005), , Proceedings of the NATO Advanced Study Institute (Montréal, 2004),

Errata to: ``Symplectic structures on fiber bundles''

Lalonde, François et McDuff, Dusa, Errata to: ``Symplectic structures on fiber bundles'' 44, 1301--1303 (2005), , Topology

A field theory for symplectic fibrations over surfaces with applications

F. Lalonde, 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

F. Lalonde and M. Pinsonnault, The topology of the space of symplectic balls in rational 4-manifolds 122, 347-397 (2004), , Duke Mathematical Journal

Symplectic and Contact Topology: Interactions and Perspectives

Y. Eliashberg, B. Khesin and F. Lalonde (eds), 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),

Length minimizing Hamiltonian paths for symplectically aspherical manifolds

Kerman, E. et Lalonde, F., Length minimizing Hamiltonian paths for symplectically aspherical manifolds 53, 1503--1526 (2003), , Ann. Inst. Fourier (Grenoble)

Symplectic structures on fiber bundles

F. Lalonde and D. McDuff, Symplectic structures on fiber bundles 42, 309-347 (2003), , Topology

Length minimising paths for symplectically aspherical manifolds

E. Kerman and F. Lalonde, Length minimising paths for symplectically aspherical manifolds 53, 1503-1526 (2003), , Ann. Inst. Fourier

Cohomological properties of ruled symplectic structures on manifolds, Mirror Symmetry IV

F. Lalonde and D. McDuff, Cohomological properties of ruled symplectic structures on manifolds, Mirror Symmetry IV 33, 79- (2002), , AMS/IP Studies in Advanced Mathematics

Groupes d'automorphismes et plongements symplectiques de boules dans les variétés rationelles

F. Lalonde and M. Pinsonnault, Groupes d'automorphismes et plongements symplectiques de boules dans les variétés rationelles 335, 931-934 (2002), , C.R. Acad. Sci. Paris, Ser. I

Holomorphic cylinders with Lagrangian boundaries and Hamiltonian dynamics

D. Gatien and F. Lalonde, Holomorphic cylinders with Lagrangian boundaries and Hamiltonian dynamics 102, 485 (2000), , Duke Mathematical Journal

Stabilisation of symplectic inequalities and applications

F. Lalonde et C. Pestieau, Stabilisation of symplectic inequalities and applications 196, 63-72 (1999), , Amer. Math. Soc. Translations, Series 2

Topological rigidity of Hamiltonian loops and quantum homology

F. Lalonde, D. McDuff and L. Polterovich, Topological rigidity of Hamiltonian loops and quantum homology 135, 369-385 (1999), , Inventiones Mathematicae

On the Flux conjectures

F. Lalonde, D. McDuff and L. Polterovich, On the Flux conjectures 15, 69-86 (1998), , CRM Proceedings and Lecture Notes, American Mathematical Society

Proceedings of the CRM Workshop on Geometry, Topology and Dynamics (Montréal 1995)

F. Lalonde (ed.), 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

J. Hurtubise and F. Lalonde (eds), 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),

Energy and capacities in symplectic topology, in:

F. Lalonde, 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

Symplectic diffeomorphisms as isometries of Hofer's norm

F. Lalonde and L. Polterovich, Symplectic diffeomorphisms as isometries of Hofer's norm 36, 711-728 (1997), , Topology

J-curves and symplectic invariants, in:

F. Lalonde, 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

F. Lalonde, New trends in symplectic geometry 19 (2), 33-50 (1997), , invited survey in the new series of C.R. Math. Rep. Acad. Sci. Canada

Positive paths in the linear symplectic group

F. Lalonde and D. McDuff, Positive paths in the linear symplectic group , 1-20 (1997), , The Arnold-Gelfand seminar, Birkhauser

J-holomorphic curves and the classification of rational and ruled symplectic 4-manifolds

F. Lalonde and D. McDuff, J-holomorphic curves and the classification of rational and ruled symplectic 4-manifolds , 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

F. Lalonde and D. McDuff, The classification of ruled symplectic 4-manifolds 3, 769-778 (1996), , Mathematical Research Letters

Errata: ``Hofer's $L^infty$-geometry: energy and stability of Hamiltonian flows. I, II''

Lalonde, F. et McDuff, D., Errata: ``Hofer's $L^infty$-geometry: energy and stability of Hamiltonian flows. I, II'' 123, 613 (1996), , Invent. Math.

Hofer's $L^{\infty}$-geometry: energy and stability of Hamiltonian flows part I

F. Lalonde and D. McDuff, Hofer's $L^{\infty}$-geometry: energy and stability of Hamiltonian flows part I 122, 1-34 (1995), , Inventiones Mathematicae

Hofer's $L^{\infty}$-geometry: energy and stability of Hamiltonian flows part II

F. Lalonde and D. McDuff, Hofer's $L^{\infty}$-geometry: energy and stability of Hamiltonian flows part II 122, 35-69 (1995), , Inventiones Mathematicae

The geometry of symplectic energy

F. Lalonde and D. McDuff, The geometry of symplectic energy 141, 349-371 (1995), , Annals of Mathematics

Local Non-Squeezing Theorems and Stability

F. Lalonde and D. McDuff, Local Non-Squeezing Theorems and Stability , 364 (1995), , Geometric and Functional Analalysis 5 (Special volume in the honour of M. Gromov)

Isotopy of symplectic balls, Gromov's radius and the structure of ruled symplectic $4$-manifolds

Lalonde, François, Isotopy of symplectic balls, Gromov's radius and the structure of ruled symplectic $4$-manifolds 300, 273--296 (1994), , Math. Ann.

Symplectic rigidity: Lagrangian submanifolds

M. Audin, F. Lalonde and L. Polterovich, Symplectic rigidity: Lagrangian submanifolds 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

F. Lalonde, Isotopy of symplectic balls, Gromov's radius, and the structure of irrational ruled symplectic 4-manifolds 300, 273-296 (1994), , Mathematische Annalen

Suppression lagrangienne de points doubles et rigidité symplectique

Lalonde, François, Suppression lagrangienne de points doubles et rigidité symplectique 36, 747--764 (1992), , J. Differential Geom.

Hamiltonian collapsing of irrational Lagrangian submanifolds with small first Betti number

Lalonde, François, Hamiltonian collapsing of irrational Lagrangian submanifolds with small first Betti number 149, 613--622 (1992), , Comm. Math. Phys.

Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents

Lalonde, François et Sikorav, Jean-Claude, Sous-variétés lagrangiennes et lagrangiennes exactes des fibrés cotangents 66, 18--33 (1991), , Comment. Math. Helv.

Classes caractéristiques isotropes

Lalonde, François, Classes caractéristiques isotropes 285, 343--351 (1989), , Math. Ann.

Homologie de Shih d'une submersion (homologies non singulières des variétés feuilletées)

Lalonde, François, Homologie de Shih d'une submersion (homologies non singulières des variétés feuilletées) , iv+101 (1987), , Mém. Soc. Math. France (N.S.)

Homologies de Shih: définition et propriétés

Lalonde, François, Homologies de Shih: définition et propriétés 39, 748--768 (1987), , Canad. J. Math.

Homologie de Shih d'une submersion

Lalonde, François, Homologie de Shih d'une submersion 299, 1025--1028 (1984), , C. R. Acad. Sci. Paris Sér. I Math.

Homologie de plongements dans les variétés différentiables

Lalonde, François, Homologie de plongements dans les variétés différentiables 299, 987--990 (1984), , C. R. Acad. Sci. Paris Sér. I Math.

Homologie de plongements dans les espaces euclidiens

Lalonde, François, Homologie de plongements dans les espaces euclidiens 297, 659--662 (1983), , C. R. Acad. Sci. Paris Sér. I Math.

Le problème d'étoiles pour graphes est NP-complet

Lalonde, François, Le problème d'étoiles pour graphes est NP-complet 33, 271--280 (1981), , Discrete Math.