March 20, 2019

Symplectic Topology, Geometry and Gauge Theory Program

Symplectic and Contact Topology, Quantum Cohomology, Symplectic Field Theory and Higher-Dimensional Gauge Theory

Topologie symplectique et de contact, cohomologie quantique, théorie des champs symplectique et théories de jauge

Part of the joint CRM-Fields Institute Symplectic Semester

March 26 to April 7, 2001
The Fields Institute, Toronto and the Centre de recherches mathématiques, Montreal


Organizing Committee/comité d'organisation:

  • S. Donaldson, London
  • B. Dubrovin, Trieste
  • Y. Eliashberg, Stanford
  • A. Givental, Berkeley
  • B. Khesin, Toronto
  • F. Lalonde, Montreal


  • the theory of Gromov-Witten invariants and quantum cohomology
  • Floer homology theories
  • relations between holomorphic curves invariants and Seiberg-Witten theory in dimensions 3 and 4
  • the study of the group of symplectic diffeomorphisms and its relations to the theory of symplectic capacities
  • symplectic field theory and higher-dimensional gauge theories

This two-week workshop will bring together researchers from symplectic topology, algebraic geometry, and mathematical physicists working in gauge theory and quantum field theory. Its main goal is to discuss the recent developments in the construction and computations of invariants of symplectic and contact manifolds and their automorphism groups, using methods of the theory of J-holomorphic curves, as well as those from gauge theory and dynamical Hamiltonian systems. The theory of these invariants is tightly related to enumerative algebraic geometry, quantum cohomology and Mirror symmetry. Recent results, of both mathematicians and physicists, manifest the existence of surprising correspondences between various gauge theories on real and complex manifolds.

The first week, to be held at the Fields Institute in Toronto, will emphasize relations of the theory of holomorphic curves with field theories, Mirror symmetries, as well as (higher dimensional) gauge theories. The second week at the CRM in Montreal will concentrate more on the geometric, analytic and dynamical aspects of symplectic topology. A train trip from Toronto to Montreal is planned as a juncture of the two parts.

The Fields Institute
222 College Street, 2nd Floor
Toronto, Ontario M5T 3J1
Telephone: (416) 348-9710
Fax: (416)348-9759


Les sujets:

  • les invariants de Gromov-Witten et la cohomologie quantique
  • les théories d'homologie de Floer
  • les relations entre les invariants construits à partir des courbes J-holomorphes et la théorie de Seiberg-Witten en dimension 3 et 4
  • l'étude des groupes de difféomorphismes symplectiques, de contact, et la théorie des capacités
  • la théorie des champs symplectique et les théories de jauge

Cet atelier de deux semaines réunira des chercheurs de topologie symplectique, de géométrie algébrique, et de physique mathématique travaillant en théorie de jauge et en théorie quantique des champs. On y discutera par exemple les développements récents dans la définition et le calcul des invariants des variétés symplectiques ou de contact, et des groupes de difféomorphismes correspondants. Les méthodes qui interviennent ici sont celles des courbes J-holomorphes, de la théorie de jauge et des systèmes hamiltoniens. Ces invariants sont étroitement liés à la géométrie énumérative, la cohomologie quantique et les symétries miroir. Des résultats récents, en mathématiques aussi bien qu'en physique, suggèrent l'existence de correspondances inattendues entre diverses théories de jauge sur les variétés réelles et complexes.

La première semaine, qui se tiendra à l'Institut Fields de Toronto, portera surtout sur les relations qu'entretiennent les courbes pseudoholomorphes avec les théories des champs, les symétries miroir, et les théories de jauge de dimension supérieure. La semaine suivante, qui se tiendra au Centre de recherches mathématiques à Montréal , portera davantage sur les méthodes géométriques, analytiques et dynamiques en topologie symplectique. Un voyage en train est prévu pour amener les participants de Toronto à Montréal durant le week-end entre les deux semaines.

Centre de recherches mathématiques

Université de Montréal
Case postale 6128, succursale centre-ville
Montréal (Québec) H3C 3J7
(514) 343-7501(telephone)
(514) 343-2254 (télécopieur)

In conjunction with this workshop there will also be a graduate course offered on 'Introduction to Symplectic Field Theory' given by Y. Eliashberg Graduate course

The 'Coxeter lectures' will be given by A. Givental Coxeter lectures

Weekend Schedule

There will be no talks scheduled on Saturday, March 31 and Sunday, April 1, 2001

Transportation Between Cities

For participants who registered before Feb.15 and whose dates include both cities, train tickets have been arranged for you. If you would like to confirm if you have a ticket please contact:

Itinerary: VIA train number 64 departs from Union station, Toronto
Saturday, March 31st at 3:35 pm
Arriving in Montreal at 8:05 pm

To make a reservation on this train call: 1-888-842-7245 or visit the website at:

Alternate transportation can be made with Greyhound bus line.

Rental car companies:


Participants are required to make your own hotel reservation. Check the Fields Institute housing page for options: TORONTO HOUSING LINK
For housing in Montreal: MONTREAL HOUSING LINK