Downloadable papers (.ps format)

(Submitted)

• Towards the geometry of double Hurwitz numbers.
• A rooted map invariant, non-orientability and Jack symmetric functions.

  2003

• Determinants of random matrices and Jack polynomials of rectangular shape.
• The matrix of chromatic joins and the Temperley-Lieb algebra.

  2002

• The quadrangulation conjecture for orientable surfaces.

  2001

• Inequivalent transitive factorizations into transpositions.
• The Gromov-Witten potential of a point, Hurwitz numbers, and Hodge integrals.
• The virtual Euler characteristic of the moduli spaces of real and complex algebraic curves.

  2000

• Transitive factorisations in the symmetric group, and combinatorial aspects of singularity theory.

  1999

• The number of ramified coverings of the sphere by the double torus. and a general form for higher genera.
• A proof of a conjecture for the number of ramified covers of the sphere by the torus.
• A combinatorial relationship between Eulerian maps and hypermaps in orientable surfaces.
• Appendix for: A combinatorial relationship between Eulerian maps and hypermaps in orientable surfaces.

  1997

• Maps in locally orientable surfaces and integrals over real symmetric matrices.
• Transitive factorisations into transpositions, and holomorphic mappings on the sphere.

  1996

• Factorisations for partition functions of random Hermitian matrix models.
• Connection coefficients, matchings, maps and a combinatorial conjecture for Jack symmetric functions.

Miscellaneous

Notes

• Map catalogue Early version of a sample of maps in "An Atlas of the Smaller Maps in Orientable and Nonorientable Surfaces," Chapman Hall/CRC, New York, 2000. (with T.I.Visentin).

  Corrigendum There is a correction to page 143 that involves map 2.113. This map has 6 rooting and there is a single map to be inserted that has 6 rootings. This does not affect the remainder of the Atlas.

• Expository notes on maps and matrix integrals Two talks that I gave in Alan Edelman's graduate seminar on matrix integrals at MIT in November 2001.

  Talks to the Canadian Mathematical Olympiad Team

• Non-commutativity and combinatorial problems Waterloo, 1998.
• Plane projective geometry (.pdf file) Waterloo, 1997.