Josh Howie

Josh Howie is an Assistant Lecturer in the School of Mathematics at Monash University. His research spans low-dimensional topology, with a focus on:

• Knot theory, including characterizations of alternating knots and links
• 3-manifolds, particularly the geometry of knot and link exteriors
• Computational methods such as A-polynomials and Ptolemy equations for studying Dehn fillings

His publication trajectory from 2017 to 2025 reveals deep specialization in geometric structures of low-dimensional manifolds, evolving from foundational characterizations of knot exteriors to advanced computational frameworks for Dehn filling operations. This work bridges algebraic invariants like character varieties with hyperbolic geometric properties, demonstrating consistent methodological innovation in topological analysis.