Dr. Francois Huard - Faculty

Research

Representation Theory of Finite Dimensional Algebras

Dr. Huard’s current research focuses on the finitistic dimension conjecture.

The finitistic dimension conjecture was first publicized by Bass in 1960. For an artin algebra A we define the finitistic dimension dimension of A to be fin.dim. A =sup {pd M such that M is a finitely generated right A-module and pd M is finite} where pd M denotes the projective dimension of M. Bass conjectured that for A as above, fin.dim. A is always finite. Since then, this conjecture has been verified for few classes of algebras. Our long term objectives are thus to better understand the finitistic dimension of an algebra, and to provide the community with new tools to study this invariant. We also want to determine new classes of algebras with finite finitistic dimension. This is of significant importance since the more diverse algebras that can be found for which the conjecture holds, the greater the chance that a general proof of the conjecture will occur. In order to achieve these goals, we study the finitistic dimension from three different perspectives. The first is through the relative homology theory developed by Auslander and Solberg. The second approach is through modules of infinite projective dimension. Finally, we study it from the point of view of stratifying systems.

Partners

Dr. Huard is a member of the Bishop’s-Sherbrooke research group in representation theory of algebras which consists of five professors and around 15 graduate students.
He is also a member of the Groud d’algèbre et théorie de nombre de l’ISM
(Institut des Sciences Mathématiques).

Student involvement

Dr. Huard is working with undergraduate students from Bishop’s University and graduate students from Université de Sherbrooke. Each year the research group gives summer research grants to undergraduate students interested in pursuing research in algebra. Since 2006, Dr. Huard organizes a mathematics camp held every two year at Bishop’s University. The 25 best CEGEP mathematics students from Québec, selected following a provincial examination, are invited to attend this unique 10 day event where the focus is put on mathematics.

Links

• Groupe de recherche en théorie des représentations des algèbres
• Colloque d’algèbre non commutative

Publications

Huard, F. “Tilted gentle algebras.” /Comm. Algebra/ 26, 63-72.

Huard, F. and Liu, S. 1999. “Tilted special biserial algebras.” /J.Algebra/ 217, 679-700.

Huard, F. and Liu, S. 1999. “Tilted string algebras.” /J. Pure and Applied Algebra,/153 (2000) 151-164

Huard, F. 2000. “One-point extensions of quasi-tilted algebras by projectives.” /Comm. Algebra, /(29) (7) (2001) 3055-3060

Huard, F. 2001. “Tilted algebras having underlying graph Dn”, Ann. Sc. Math. Québec

Brewster, R., Dedic R. and Huard, F. 2005. “Edge coloured homomorphisms and the recognition of bound quivers” /Discrete Math/(297) (2005) 13-25

Huard, F., Lanzilotta M. and Mendoza O. 2007. “A new approach to the finitistic dimension” J. Algebra

Huard, F., Lanzilotta M. and Mendoza O. 2007. “Finitistic dimension through infinite projective dimension” Bulletin of the London Math. Soc.