Students and postdoctoral fellows

Prospective graduate and NSERC summer students:

Students who want to work with me should have a good knowledge in algebra (a 3rd year algebra course, e.g., the University of Ottawa course MAT 3143) or linear algebra (3rd year course in linear algebra, e.g. the University of Ottawa course MAT 3141). If you are interested and/or want to know more, please send me an email. I'll be happy to discuss possible projects with you.

Information on the department's graduate program is given here. Below is a short description of possible thesis projects for students working under my supervision. Theses can be written in French or English.

Projects on root systems (M.Sc. or NSERC summer students): Root systems are certain finite sets of vectors in Euclidean space which have a lot of symmetries. They arise naturally in the study of Lie algebras and the corresponding groups. A good reference is Chapter III of J. Humphreys' book ``Introduction to Lie Algebras and Representation Theory''. The projects could be related to my recent AMS memoir with O. Loos on locally finite root systems, in which we generalize the theory to infinite root systems or my preprint on ``Reflection systems and partial root systems'', posted on my preprints page.

Ph.D. projects on Lie algebras: These projects will build on my recent work as well as the work of my recent Ph.D. students in the area of root-graded Lie algebras and extended affine Lie algebras. An introduction to these areas will be provided through lecture and reading courses, but a good knowledge of the structure theory of finite-dimensional Lie algebras, e.g. Chapters I -- VI of Humphreys' book mentioned above, would be very helpful.

My students and postdoctoral fellows have a weekly seminar on various topics related to Lie algebras. Some past examples are representation theory of semisimple Lie algebras or quantum groups. Everybody interested is very welcome to participate, just send me an email.

Present students and postdoctoral fellow:

  • Negin Mehrdad (M.Sc.)
  • Marc-Antoine Leclerc (M.Sc., co-supervision with Kirill Zaynullin)
  • Sanghoon Baek (postdoctoral fellow, co-supervision with Kirill Zaynullin)
  • Khoa Pham (undergraduate student, UoO work study program)

    Past NSERC undergraduate summer students:

  • Miriam Grimberg (summer 2010)
  • Jerome Lefebvre (summer 2008)
  • Emilie Richer, (summers 2002 and 2003)
  • Lynn Shaddick, (summers 2002 and 2003)

    • M.Sc. theses supervised:

  • Caroline El-Chaar (2010, co-supervision with Alistair Savage): The Onsager algebra

    Ph.D. theses supervised:

  • Angelika Welte (2009): Central extensions of graded Lie algebras.
  • Samina Bashir (2008): Automorphisms of simple anti-Jordan pairs.
  • Ana Duff (2002): Derivations, invariant forms and the second homology group of orthosymplectic Lie superalgebras.
  • Yoji Yoshii (1999): The coordinate algebra of extended affine Lie algebras of type A1.

    • Recent Postdoctoral fellows:

  • Juana Sanchez Ortega (January 2010 - July 2010), research interests: associative and Lie algebras.
  • Simon Huggenberger (January-February 2010), research interests: incidence geometry and Jordan pairs.
  • Angelika Welte (January 2010-August 2010), research interests: central extensions of root-graded Lie algebras
  • Jie Sun (September 2009 - August 2010), research interests: central extensions of Lie algebras, Galois descent.
  • Prasad Senesi (January 2008 - July 2009, co-supervision with Alistair Savage), research interests: affine Lie algebras.
  • Daniel Mondoc (May and June 2007), research interests: Kantor triple systems
  • Irene Paniello (March - July 2006, March-July 2007, May - July 2008), research interests: Jordan structures
  • Malihe Yousofzadeh (October 2005 - March 2006), research interests: Extended affine Lie algebras
  • Michael Lau (July 2004 - April 2007), NSERC PDF (January 2005-December 2006), research interests: representations of Lie algebras, cyclic homology
  • Maribel Tocon (January 2004 - November 2006), research interests: Jordan and Lie algebras
  • Xueqing Chen (July 2002 - June 2004), NSERC PDF, research interests: associative algebras and Lie theory
  • Esther Garcia Gonzalez (Fall term 2000), research interests: Jordan algebras