David M. Jackson
(= David M.R. Jackson)
Dept. of Combinatorics & Optimization
University of Waterloo
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I graduated from Cambridge in 1970 with a PhD in mathematics.
After spending two years as an Assistant Professor at Cornell, I moved
to the Department of Combinatorics and Optimization in Waterloo.
In 1992 Chris Godsil, Ian Goulden and I founded the
Journal of Algebraic Combinatorics and stepped down as
managing editors after ten years of service.
I am on the editoral boards of several journals and was, for many
years, a mathematical consultant to the Oxford English Dictionary
I am a Fellow of the Royal Society of Canada
and a Member of the Academy of Mathematical and Physical Sciences.
- This page was updated on 6 April 2014.
by Goulden and Jackson,
is now available as a paperback from Dover Publications.
The .ps files of a number of papers
can be found in PREPRINTS .
This has been discontinued since the papers are available on the mathArchive.
A list of
I) submitted papers,
II) papers in preparation,
III) books, and
IV) published papers may be found in
PUBLISHED PAPERS .
Research area: algebraic and enumerative combinatorics: application
of these to questions in algebraic geometry, and perturbative quantum field theory.
Current general interest: the use of algebraic and analytic ideas,
together with combinatorial constructions, in questions that have an
enumerative aspect; enumerative questions that arise in algebraic
geometry and mathematical physics.
Current and nascent research projects:
- integrable hierarchies and the Join-Cut Equation;
- using enumerative techniques to find a generalisation of the
Ekedahl-Lando-Shapiro-Vainshtein theorem to the double Hurwitz problem;
- the "b-conjecture": this involves a conjectured invariant of (rooted)
maps (2-cell embeddings of graphs) interpolating naturally between
the moduli spaces of real and complex curves; "b" is associated with
Jack symmetric functions;
- the combinatorics of the beta-Jacobi density function in the context of maps (2-cell embeddings of graphs);
- diagrammatics of 3-manifolds;
- constructive aspects of perturbative quantum field theory, algebraic and combinatorial
aspects of the Legendre and Fourier transforms in this context;
- the study of quantum invariants and Vassiliev invariants of knots as a means of eliciting
properties of Lie algebras and Hopf algebras in the context of enumerative combinatorics.
Graduate Students and thesis titles
- (M.M) R. Tessier.
Path tableaux and the combinatorics of the immanant function.
- (Ph.D) C.A. Sloss.
Enumeration of factorizations in the symmetric group:
from centrality to non-centrality.
- (Ph.D) M.A. La Croix.
The combinatorics of the Jack parameter and
the genus series for topological maps.
- (M.Math)(thesis) M. Yip,
Genus one partitions.
- (M.Math)(thesis) C.A. Sloss,
Enumeration of walks on generalized differential posets.
- (Ph.D) J.C.Irving.
Combinatorial constructions for transitive factorizations
in the symmetric group.
- (M.Math)(essay) M.A. La Croix,
Approaches to the enumerative theory of meanders.
- (M.Math)(thesis) L.L. Mac Donald,
The Eulerian subalgebra of Solomon's descent algebra and
- (Ph.D) D.R.L.Brown,
Differential equations and depth-first search for the enumeration
of maps in surfaces.
- (M.Math)(essay) J.C.Irving.
An enumeration problem concerning products of permutations.
- (Ph.D) D.G.C.Horrocks,
Sperner properties of filters generated by two-sets in
- (M.Math) (essay) D.R.L.Brown.
On locally orientable maps, integral representations and monopoles.
- (Ph.D) T.I.Visentin,
A character theoretic approach to the study of combinatorial properties
of maps in orientable surfaces.
- (M.Math) (essay) D.Horrocks,
- (M.Math) (essay) T.I.Visentin,
Ordered sets of non-intersecting lattice paths.
- (Ph.D) J.S.Devitt,
The algebraic manipulation of certain enumerative constructions.
- (Ph.D) I.P.Goulden,
Combinatorial decompositions in the theory of algebraic
- (Ph.D) J.W.Reilly,
An enumerative theory of formal power series. (1977).
- (M.Math) (essay) S.C. Locke. (1976)
- (M.Math) W.L.Kocay, (1976).
- (M.Math) M.R.Lipford.
Fundamental problems in pattern recognition (1975).
- (M.Math) (essay) G.H.J. van Rees. (1974)
My work address is:
Professor David M.R. Jackson
Department of Combinatorics and Optimization
Faculty of Mathematics
University of Waterloo
Waterloo, Ontario, CANADA, N2L 3G1
Fax: (519) 725-5441
Tel: (519) 888-4056