David Jackson

Algebraic combinatorics

David Jackson is exploring the way in which algebraic combinatorics can be used to make headway on classical problems in algebraic geometry. Faber’s conjecture has known proofs, but they are very, very long. Professor Jackson is working on a natural, more accessible proof, related to mathematical physics and mathematics, for this classical theorem.

Other explorations in planar algebra – related to the four color theorem – are productive and motivating for Jackson. New methods and conjectures have opened the problem to algebraic investigation and Professor Jackson is looking forward to examining the problem with new perspective.

In 2004, Jackson co-developed (with I. Goulden, UWaterloo and R. Vakil, Stanford) a very nice proof for the Hurwitz problem, open since 1890. "Combinatorial Enumeration" by Goulden and Jackson was reprinted in 2004 (in a Dover edition) at the request of the mathematics community. The book is currently used as a reference book for the enumerative side of statistical mechanics at Harvard.

University of Waterloo Mathematics, Annual Report 2004