Jacques Hurtubise BSc. (UdeM), D.Phil. (Oxford)
  hurtubise@math.mcgill.ca

  Tel: (514) 398-3816

    Courses | Research Interests | Publications | Awards | Graduate Students | CV | Download   << Back 

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Dept. of Mathematics, McGill University
Burnside Hall, 805 Sherbrooke St. W.
Montreal, Que. H3A 2K6



COURSES

Fall 2007

          MATH 315 - Ordinary differential equations

Winter 2008

          MATH 263 - Linear algebra and differential equations

          MATH 380 - Honours differential geometry



RESEARCH INTERESTS

  1. Topology of moduli spaces.
  2. Geometry of integrable systems.
  3. Moduli spaces on Riemann surfaces.

PUBLICATIONS


(Click name to download in TeX format - see Download section below for further instructions and required style files, including vanilla.sty)

Recent Journal Articles

42. Calorons, Nahm's equations on $S^1$ and bundles over $P^1xP^1$, (with B. Charbonneau) math.DG/0610804, 33p.

41. Separation of Variables and the Geometry of Jacobians, SIGMA 3 (2007), 017, 14 pages; math-ph/0702032

40. Group-valued Implosion and Parabolic Structures (with Lisa Jeffrey, Reyer Sjamaar) Amer. J. Math.  128  (2006),  no. 1, 167--214

39.  Moduli of framed parabolic sheaves(with Lisa Jeffrey, Reyer Sjamaar), Ann. Global Anal. Geom.  28  (2005),  no. 4, 351--370.

38. The geometry of the Calogero-Moser system (with  T. Nevins),  Ann. Inst. Fourier (Grenoble)  55  (2005),  no. 6, 2091--2116.

37.  Elliptic Sklyanin integrable systems for arbitrary reductive groups (with E. Markman)  Adv. Theor. Math. Phys.  6  (2002),  no. 5, 873--978  math.AG/0203031

36. Surfaces and the Sklyanin bracket (with E. Markman)  Commun. Math. Phys. 230, 485-502 (2002) math.AG/0107010

35.  Calogero-Moser systems and Hitchin systems (with E. Markman) Commun. Math. Phys 223, 533-552 (2001). AG/9912161


34. Stability theorems for spaces of rational curves (with C.P. Boyer and R.J. Milgram), Int'l Journal of Mathematics 12No.2 (2001), 223 - 262. AG/990309

33. Representations with Weighted Frames and Framed Parabolic Bundles (with Lisa Jeffrey) Canad. J. Math. 52 (2000), no. 6, 1235--1268. SG/9906026 SG/9906026

32. Darboux coordinates, generalised Hitchin systems and the classical r-matrices. (with Mounia Kjiri) Commun. Math. Phys., 210 (2000) 2, 521-540

31. Particles and connections on a four-manifold, Commun. Anal. Geom., 7 (1999), 55-93.

30. Rank 2 integrable systems of Prym varieties (with E. Markman), Adv. Theo. Math. Phys.,2 (1998), 633-695.

29. The algebraic geometry of the Kostant-Kirillov form, J. Lond. Math.Soc. (2) 56 (1997), 504-518.

28. Darboux coordinates on coadjoint orbits in Lie algebras, (with M. Adams and J. Harnad) Lett. Math.Phys. 40 (1997), 41-57

27. Integrable systems and algebraic surfaces, Duke Mathematical Journal 83, 19-50 (1996); Erratum, 84, 815 (1996)

26. Holomorphic maps of a Riemann surface into a flag manifold, J. Diff. Geom. 43, 99-118 (1996)

25. The Atiyah-Jones conjecture for ruled surfaces, (with R.J. Milgram) J. fur die Reine und Ang. Math. 466, 111-143 (1995)

24. Configurations de particules et espaces de modules, Can. Math. Bulletin 38, 66-79 (1995)

23. The topology of the space of rational maps into generalized flag manifolds (with C.P. Boyer, B.M. Mann and R.J. Milgram) Acta Mathematica 173, 61-101 (1994).

22. Finite Dimensional Coadjoint Orbits in a Loop Algebra Lett. Math. Phys. 30, 99-104 (1994)

21. Darboux coordinates and Liouville-Arnold integration in loop algebras (with M. Adams and J. Harnad) Commun. Math. Phys. 155, 385-413 (1993)

20. Quantification de la cohomologie des algèbres de Lie de champs de vecteurs et fibrés en droites sur des surfaces algébriques complexes (with A. Gonzalo-Lopez, N.Kamran and Peter Olver) C. R.Acad.Sci. Paris.,t.316, S6rie 1, ppl3O7-1312 (1993).

19. The topology of instanton moduli spaces. 1: The Atiyah-Jones conjecture (with C.P. Boyer, B.M. Mann and R.J. Milgram), Annals of Math., 137, 561-609 (1993)

18. The Atiyah-Jones conjecture (with C.P. Boyer, B.M. Mann and R.J. Milgram), Bull. AMS. 26, 317-321 (1992)

Book Chapters

3. Stability Theorems for Moduli Spaces. CMS-SMC 50th Anniversary volume 3, Invited Papers, ppl53172, 1997

2. Liouville Generating Functions for Isospectral Flow in Loop Algebras, (with M. Adams and J. Harnad) in "Integrable and Superintegrable Systems , ed. B. Kuperschmidt, World Scientific, Singapore, 1990.

1. Russian translations of articles in "Monopoles, Topological and Variational Methods", MIR, Moscow, 1989.


AWARDS


  • 1975 - Governor General's Medal
  • 1978 - Prix Georges Baril, Université de Montréal
  • 1978-81 - Rhodes Scholarship
  • 1987 - 88 Fellowship, Institute for Advanced Study, Princeton, N.J.
  • 1993-94 - American Mathematical Society Centennial Fellow
  • 1993 - Coxeter-James Lecturer, Canadian Mathematical Society
  • 2004 - Fellow, Royal Society of Canada

GRADUATE STUDENTS


Masters theses supervised

1. F. Renaud (1985) Linéarisation de champs de vecteurs.

2. F. Beaudet (1986) Harmonicité et invariants.

3. D. Labrecque (1987) Régularité des solutions de problèmes variationnels.

4. S. New (1990), Hamiltonian systems and loop groups applied to equations of KdV type.

5. C. Anand (1990), Harmonic maps.

6. M. Mizerski (joint) (2000),   Singularities of Schubert Varieties

7. N. Lehmann, 2006,  Integrable systems

Doctoral theses supervised.

1. R.Bielawski (1993; professor at Leeds) Monopole metrics and rational functions.

2. C. Anand (1994; professor at McMaster), On the construction of Unitons.

3. S. New (1997; lecturer at the University of Waterloo)) Deformations of vector bundles over the Riemann sphere.

4. F. Jetzer (1999; professor at Collége Militaire de St.Jean) " Integrable Hamiltonian Systems on Supermanifolds'

5. M. Kjiri (2000) "Systèmes de Hitchin généralisés et variétés symplectiques" (Université de Montréal)

6.  R. Moraru (2000; Professor at U. Waterloo) ``Moduli of vector bundles over a Hopf surface, and their stability properties.

Post-Doctoral students supervised (*= joint supervision)

Arleigh Crawford (1992-94) C. Anand (1994-95), K. Guruprasad (1994-95), D. Nguyen (1994-96), A. Wisse (1994-95), E. Markman (1995-96), S. Kallel (1994-97), A. Lebel (1996-98)B. Anchouche (1998-00), M. Bertola (*)(00-02),
D. Matessi (*) (01-02),  R. Moraru (2001-02), R. Mohammadalikhani (02-04), S. Starr(2003-04) (*),  Mo Man Yue (*) (2003-05), Benoit Charbonneau (04-07).

Masters students under current supervision.

S. Miscione

Doctoral students under current supervision.

M. Wong



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