David M. Jackson (= David M.R. Jackson)

Dept. of Combinatorics & Optimization

University of Waterloo

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Abbreviated c.v.

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 Project.

I am a Fellow of the Royal Society of Canada and a Member of the Academy of Mathematical and Physical Sciences.

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Recent Developments

• This page was updated on December 2019.
• Combinatorial Enumeration, by Goulden and Jackson, is now available as a paperback from Dover Publications.

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Publications

For a full publication list, please see my Google Scholar page.

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 .

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Research interests

• 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:
  1. integrable hierarchies and the Join-Cut Equation;
  2. using enumerative techniques to find a generalisation of the Ekedahl-Lando-Shapiro-Vainshtein theorem to the double Hurwitz problem;
  3. 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;
  4. the combinatorics of the beta-Jacobi density function in the context of maps (2-cell embeddings of graphs);
  5. diagrammatics of 3-manifolds;
  6. constructive aspects of perturbative quantum field theory, algebraic and combinatorial aspects of the Legendre and Fourier transforms in this context;
  7. 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.

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  Graduate Students and thesis titles

  • (M.Math)(thesis) R. Tessier. Path tableaux and the combinatorics of the immanant function. (2013)
  • (Ph.D) C.A. Sloss. Enumeration of factorizations in the symmetric group: from centrality to non-centrality. (2011)
  • (Ph.D) M.A. La Croix. The combinatorics of the Jack parameter and the genus series for topological maps. (2009)
  • (M.Math)(thesis) M. Yip, Genus one partitions. (2006)
  • (M.Math)(thesis) C.A. Sloss, Enumeration of walks on generalized differential posets. (2005)
  • (Ph.D) J.C.Irving. Combinatorial constructions for transitive factorizations in the symmetric group. (2004)
  • (M.Math)(essay) M.A. La Croix, Approaches to the enumerative theory of meanders. (2003)
  • (M.Math)(thesis) L.L. Mac Donald, The Eulerian subalgebra of Solomon's descent algebra and its idempotents. (2002)
  • (Ph.D) D.R.L.Brown, Differential equations and depth-first search for the enumeration of maps in surfaces. (2000)
  • (M.Math)(essay) J.C.Irving. An enumeration problem concerning products of permutations. (1998)
  • (Ph.D) D.G.C.Horrocks, Sperner properties of filters generated by two-sets in Boolean algebras. (1995)
  • (M.Math) (essay) D.R.L.Brown. On locally orientable maps, integral representations and monopoles. (1995)
  • (Ph.D) T.I.Visentin, A character theoretic approach to the study of combinatorial properties of maps in orientable surfaces. (1989)
  • (M.Math) (essay) D.Horrocks, q-counting. (1989)
  • (M.Math) (essay) T.I.Visentin, Ordered sets of non-intersecting lattice paths. (1983)
  • (Ph.D) J.S.Devitt, The algebraic manipulation of certain enumerative constructions. (1981)
  • (Ph.D) I.P.Goulden, Combinatorial decompositions in the theory of algebraic enumeration. (1979).
  • (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)

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  Other projects

  The following translations from Welsh into English, are work in progress. I hope to find the time to complete them in the near future.
  • Chwalfa by T. Rowland Hughes (Gwasg Aberystwyth - 1946).

    The word "Chwalfa" has several meanings, including "Destruction", but the one that best captures one of the powerful themes is `Wilderness'. The novel opens with the wilderness of a mountainous region, the ultimate significance of which develops slowly though the novel, and is set during a strike at the slate quarry in a fictional village called Llechfaen. There are many references to well known politicians and literary figures of the era. The author has made use of some of the published accounts of certain events associated with the Great Strike that took place in the Penrhyn Quarry in North Wales in the period 1901 to 1903. The strike was one of the largest experienced in the industrial history of Britain. The events are seen through the experiences of the extended family of Edward Ifans, who is a quarryman, and his wife, Martha. The novel gives a vivid account of cultural and social life in North Wales and in South Wales during these exceptional times.

  • Y Dylluan Wen by Angharad Jones (Gwasg Gomer, Llandysul, Ceredigion - 2013)

    (Enillydd y Fedal Rhyddiaith yn Eisteddfod Genedlaethol Frenhinol Cymru 1995)

    While set in the modern era, "The White Owl" opens with a reference to "Gwydion", and therefore to the "Mabinogi," a collection of stories of great antiquity that are associated with Wales, and continue to be the subject of scholarly research in Celtic Studies. They remain, however, less familiar outside Wales. While the novella may at first appear to be a dark and brooding account of events within a small village, the reader is drawn gradually towards complexities that demand contemplation, that haunt the imagination and the intellect, and that have meaning beyond the confines of the village itself. In an as yet unfinished commentary I have endeavoured to provide sufficient detail from the Mabinogi, and from other sources (including the Eleusinian Mysteries, and a few of the techniques of probing the text of the Mabinogi), to reveal enough of the substrate upon which I believe parts of the novel rest. The commentary is an account of my own reading and understanding of the novella: others will have their own understanding of it.

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  Personal

  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
  

  Misc. info:

  Email:  dmjackso@uwaterloo.ca
  Fax:   (519) 725-5441
  Tel:   (519) 888-4056