François Lalonde

François Lalonde (born 17 September 1955) is a Canadian mathematician, specializing in symplectic geometry and symplectic topology.

Lalonde received from the University of Montreal in 1976 his bachelor's degree in physics and in 1979 his master's degree in logic and computer science. In 1985 he received his doctorate (Doctorat d'Etat) in mathematics from the University of Paris-Sud in Orsay [1] becoming one of the rare candidates obtaining the Doctorat d'Etat before the age of thirty. He then was an NSERC University Research Fellow at Université du Québec à Montréal where he became full professor in 1991 until 2001. He is professor at the University of Montreal since 2001, holding the Canada Research Chair in symplectic topology.[2]

He has held invited positions at many institutions, including the École Normale Supérieure in Lyon (2008), Stanford University (2005), IHES (1983–1985), Harvard University (1989–1990), the University of Strasbourg (1990), the École Polytechnique (2001-2002), the University of Tel Aviv (1997 and 1999), and the University of Aix-Marseille (2015).[2]

With Octav Cornea he developed a new homology (cluster homology), leading to a new universal Floer homology for pairs of Lagrangian submanifolds of a symplectic manifold.[3] He has also collaborated with Dusa McDuff and Leonid Polterovich.

He became Fellow of the Royal Society of Canada in 1997, Fellow of the Fields Institute in 2001. From 2000 to 2001 he was a Killam Fellow. From 2004 to 2008 and from 2011 to 2013 he was the director of the Centre de Recherches Mathématiques (CRM) in Canada. He (co)founded several institutions, namely the Institut des Sciences Mathématiques (ISM) (McGill, Montreal, UQAM, Concordia, Laval, Sherbrooke universities) with Francis Clarke, the Centre interuniversitaire de recherches en géométrie différentielle et en topologie (CIRGET), the Institut transdisciplinaire de recherches en informatique quantique (INTRIQ) with Gilles Brassard and Michael Hilke, and the journal Annales mathématiques du Québec (Springer).

In 2005, he was the Stanford Distinguished Lecturer and the Andreas Floer Memorial Lecturer (UC Berkeley). In 2006 he was an Invited Speaker with talk Lagrangian submanifolds: from the local model to the cluster complex at the ICM in Madrid.

Selected publications

  • New trends in symplectic geometry, C.R. Math. Rep. Acad. Sci. Canada, New Series, vol. 19, 1997, pp. 33–50
  • with Dusa McDuff and Leonid Polterovich: Topological rigidity of Hamiltonian loops and quantum homology, Inventiones Mathematicae, vol. 135, 1999, pp. 369–385
  • with McDuff: The geometry of symplectic energy, Annals of Mathematics, vol. 141, 1995, pp. 349–371
  • with McDuff: Hofer's -geometry: energy and stability of Hamiltonian flows, Inventiones Mathematicae, vol. 122, 1995, parts 1,2, pp. 1–34, 35–69
  • with McDuff: J-holomorphic curves and the classification of rational and ruled symplectic 4-manifolds, in C. B. Thomas (ed.) Symplectic and Contact Geometry, Cambridge University Press 1996
  • Energy and capacities in symplectic topology, in W.H. Kazoo (ed.) Geometric Topology, Studies in Advanced Mathematics, American Mathematical Society/International Press, vol. 2, 1997, pp. 328–374
  • with McDuff: Local Non-Squeezing Theorems and Stability, Geometric and Functional Analalysis, vol. 5, 1995, p. 364 (Gromov-Volume)
  • with Michèle Audin and L. Polterovich: Symplectic rigidity: Lagrangian submanifolds, in M. Audin, J. Lafontaine (eds.), Holomorphic Curves in Symplectic Geometry, Progress in Mathematics, vol. 117, 1995, pp. 271–322
  • with Shengda Hu: A relative Seidel morphism and the Albers map, Trans. Amer. Math. Soc. 362 (2010), pp. 1135–1168 doi:10.1090/S0002-9947-09-04986-1

as editor:

  • with Miguel Abreu and Leonid Polterovich (eds.): New Perspectives and Challenges in Symplectic Field Theory, The CRM Proceedings and Lecture Notes 49, 342 (2009)
  • with Paul Biran and O. Cornea (eds.): Morse theoretical methods in symplectic topology and non-linear analysis, Proceedings of the NATO Advanced Study Institute (Montréal, 2004), Kluwer Academic Publishers, Dordrecht (2005)
  • with Yakov Eliashberg and Boris Khesin (eds.): Symplectic and Contact Topology: Interactions and Perspectives, Proceedings of the workshop on Symplectic topology and higher dimensional Gauge invariants (held at the Fields Institute in March-April 2001), Fields Institute Communications 35, AMS (2003)
  • as sole editor: Proceedings of the CRM Workshop on Geometry, Topology and Dynamics (Montréal 1995), CRM Proceedings and Lecture Notes 15, AMS (1998)
  • with Jacques Hurtubise (ed.): Gauge Theory and Symplectic Geometry, Proceedings of the NATO Summer Advanced Institute on Gauge Theory and Symplectic Geometry (Montréal 1995), Kluwer Academic Publishers, Dordrecht (1997) (containing Lalonde's contribution J-curves and symplectic invariants)

References

  1. ↑ Lalonde, François. "Homologie non-singulières d'une variété et homologie sectionelle d'une submersion". theses.fr.
  2. 1 2 "C. V. — François Lalonde, University of Montreal" (PDF).
  3. ↑ Cornea, Lalonde Cluster Homology, Preprint 2005
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