François Bergeron

Member of Laboratoire de Combinatoire et d'Informatique mathématique,
Professor, Department of Mathematics,
Université du Québec à Montréal.

(vers la Page en français )

School April 30-May 4, 2007: Combinatorial Hopf Algebras and Macdonald Polynomials
Workshop May 7-11, 2007: Combinatorial Hopf Algebras and Macdonald Polynomials
School May 21-25, 2007: Algebraic Geometry and Algebraic Combinatorics
Workshop May 28- June 1, 2007: Interactions between Algebraic Combinatorics and Algebraic Geometry

General audience talks.

• Why is algebraic combinatorics so hot?
  Pourquoi la combinatoire algébrique est-elle si cool? (PDF) (CCÉM/CUMC, Kingston, 2005)
• Les mathématiques au secours de l'art d'Escher (PDF) (No animation, 6.9 meg. In French. This presentation was prepared using material taken from the web site: Escher and the Droste effect. Other relevant material.)
• Une exploration visuelle des mathématiques (PDF) (No animation, 7.1 meg. In French. This presentation was prepared using material coming from many web sites. Here is a partial list of these sites.)
• Introduction à la cryptographie (HTML) (General talk. In French)

Transparencies of Recent Talks

• Harmonics for Steenrod Operators, (Session: Algebraic Combinatorics, CMS Winter Meeting, Toronto, 2006)
• A Combinatorial Moduli Space for Polynomials of Degree n (Workshop on Computational and Combinatorial Commutative Algebra, Fields, 2006)
• Is k-QSym free over Sym? (PDF) (FPSAC'05, Special session in honour of Adriano Garsia, Taormina, Sicily, Italy, 2005)
• Diagonal coinvariants: what's up? (PDF) (Mittag-Leffler Institut, Sweden, 2005)
• Species: a modern approach to combinatorics (PDF) (Uppsala universitet, Department of Mathematics Colloquium, Sweden, 2005)
• Positive differences of products of Schur functions (PDF) (The University of Michigan Combinatorics Seminar, Ann Arbor, 2004)
• Species and Variations on the Theme of Species (PDF) (CTCS'04, Copenhague, 2004)
• Invariants of Finite Groups and Their Applications to Combinatorics (25 years later) (PDF) (CRM-ISM Colloquium, 2004)
• A Conjecture of Fomin-Fulton-Li-Poon (PDF) (Dartmouth Math Colloquium, 2003)
• Diagonal Alternants (PDF) ( Recent advances in algebraic and enumerative combinatorics, Banff, 2003)
• Quasi-symmetric Polynomials (PDF) ( MIT, Applied Math Colloquium, Boston, 2002)

Research Areas

• Diagonal Harmonics of the Symmetric Group and Macdonald Polynomials. 
• Descent Algebras and Noncommutative Symmetric Functions. 
• Enumerative Combinatorics (Book on the Theory of Species.)
• Interactions between algebraic combinatorics and algebraic geometry.

Current and past students

Recent Papers

• Tensorial square of the Hyperoctahedral group Coinvariant Space
  (with R. Biagioli), Submitted. ArXiv: math.CO/0412456.
  
• Diagonal Temperley-Lieb Invariants and Harmonics
  (with J.-C. Aval and N. Bergeron), Submitted. ArXiv: math.CO/0411568
  
• Inequalities Between Littlewood-Richardson Coefficients
  (with R. Biagioli and M. Rosas), Accepted for publication (2005), Journal of Combinatorial Theorie, Series A.
  
• Some Positive Differences of Products of Schur Functions,
  (with P. McNamara), ArXiv: math.CO/0412289.
  
• Decomposition of the Diagonal Action of S_n on the Coinvariant Space of S_n x S_n
  (with F. Lamontagne), Lascoux FestSchrift, Séminaire Lotharingien de Combinatoire, Issue 52, (2004).
  
• Ideals of quasi-symmetric functions and super-covariant polynomials for S_n
  (with J.-C. Aval and N. Bergeron), Advances in Mathematics, Volume 181, Issues 2, (2004), 353-367.
  
• Lattice Diagram Polynomials in One Set of Variables,
  (with J.-C. Aval and N. Bergeron), Special number of Advances Applied Mathematics, to the memory of
  Rodica Simion, Volume 28, Issues 3-4, (2002), 343-359.
  
• Multiple Left Regular Representations Generated by Alternants,
  (avec A. M. Garsia, et G. Tesler), Special number of Journal of Combinatorial Theory
  to the memory of Gian-Carlo Rota, , Series A 91, 49-83 (2000).
  
• Intersection of Modules Related to Macdonald's Polynomials
  (with S. Hamel), Discrete Mathematics 217 (2000), 51-64.
  
• Counting Young Tableaux of Bounded Height,
  (with F. Gascon), Journal of Integer Sequences, Volume 3 (2000), Article 00.1.7.
  
• Identities and Positivity Conjectures for Some Remarkable Operators in the Theory of Symmetric Functions
  (with A. M. Garsia, M. Haiman and G. Tesler), Methods and Applications of Analysis, Volume 6, No. 3, (1999), 363-420.
  (Note that preprints wrongly mention Asian J. Math.)
  
• Lattice Diagram Polynomials and Extended Pieri Rules
  (with N. Bergeron, A. M. Garsia, M. Haiman and G. Tesler), Advances in Mathematics, Volume 142, (1999), 244-234.
• Science Fiction and Macdonald's Polynomials
  (with A. M. Garsia), In: Algebraic Methods and q-Special Functions, R. Floreanini, L. Vinet (eds.), CRM Proceedings & Lecture Notes, American Mathematical Society, Volume 22, (1999), 1-52.
  
• Acyclic Complexes Related to Noncommutative symmetric Functions
  (with D. Krob), Journal of Algebraic Combinatorics, (1997), 103-107.
  
• Standard Paths in the Composition Poset
  (with M. Bousquet-Mélou and S. Dulucq), Annales des sciences mathématiques du Qu?bec, Volume 19, (1995), 139-151.
• Constructibly Differentially Algebraic Series in Several Variables
  (with U. Sattler), Theoretical Computer Science, Volume 144, (1995), 59-65.
  
• Conjectures on the Enumeration of Tableaux of Bounded Height (.pdf)
  (with L. Favreau and D. Krob), Discrete Math., Volume 139, (1995), 463-468.
• Fourier Transform for Some Semisimple Algebras and Harmonic Analysis for Probabilistic Algorithms (.pdf)
  (with L. Favreau), Discrete Math., Volume 139, (1995), 19-32.
• Efficient Computation of Addition Chains
  (with J. Berstel et S. Brlek), Journal de théorie des nombres de Bordeaux, Volume 6, (1994), 21-38.
• Surprising Mathematics Using a Computer Algebra System ,
  Jour. Symbolic Computation, Volume 15, (1993), 365-370.
• A Decomposition of the Descent Algebra of Finite Coxeter Groups,
  (with N. Bergeron, B. Howlett and D. Taylor), J. of Algebraic Combinatorics, Volume 1, (1992), 23-42.
  
• Homomorphisms Between Solomon's Descent Algebras,
  (with A. M. Garsia and C. Reutenauer), J. of Algebra Volume 150, (1992), 503-519.
  
• A Decomposition of the Descent Algebra of the Hyperoctahedral Group I,
  (with N. Bergeron), J. of Algebra Volume 148, (1992), 86-97.
  
• Varieties of Increasing Trees,
  (with Ph. Flajolet and B. Salvy), Proc. CAAP'92, Ed.: J.-C. Raoult, Lect. Notes in Comp. Sc., No. 581, Springer-Verlag, (1992), 24-48.
• Computing the Generating Function of a Series Given its First Few Terms (.pdf)
  (with S. Plouffe), Experimental Mathematics , Volume 1, (1992), 307-312.
• Orthogonal Idempotents in the Descent Algebra of B_n and Applications
  (with N. Bergeron), Jour. of Pure and Applied Algebra Volume 79, (1992), 109-129.

How to come and visit me:
Office (see this map): Pavillon Président Kennedy  PK-4240 (Lattitude 45°30'32.03"N, Longitude: 73°34'6.94"W)
           201, avenue du Président-Kennedy
           Montréal (Québec) H2X 3Y7

Telephone: (514) 987-3000  Ext.: 3958#                            Fax: (514) 987-8274

Electronic mail: