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Combinatorial Approaches To The Jacobian Conjecture

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Date

2007-08-24T17:21:07Z

Authors

Omar, Mohamed

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University of Waterloo

Abstract

The Jacobian Conjecture is a long-standing open problem in algebraic geometry. Though the problem is inherently algebraic, it crops up in fields throughout mathematics including perturbation theory, quantum field theory and combinatorics. This thesis is a unified treatment of the combinatorial approaches toward resolving the conjecture, particularly investigating the work done by Wright and Singer. Along with surveying their contributions, we present new proofs of their theorems and motivate their constructions. We also resolve the Symmetric Cubic Linear case, and present new conjectures whose resolution would prove the Jacobian Conjecture to be true.

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Keywords

Jacobian Conjecture, Bass-Connell-Wright Tree Inversion Formula, Catalan Tree Inversion Formula

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http://hdl.handle.net/10012/3181

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Theses
Combinatorics and Optimization