Research

My research is in low-dimensional topology. I spend most of my time studying surfaces in knot complements and 3-manifolds.

Articles

1. A characterisation of alternating knot exteriors, Geom. Topol. 2017. arXiv journal

2. (w. Jessica Purcell) Geometry of alternating links on surfaces, Trans. Amer. Math. Soc. 2020. arXiv journal

3. (w. Dan Mathews, Jessica Purcell & Em Thompson) A-polynomials of fillings of the Whitehead sister, Int. J. Math. 2023. arXiv journal 

4. (w. Dan Mathews & Jessica Purcell) A-polynomials, Ptolemy equations and Dehn filling, Algebr. Geom. Topol. (accepted) arXiv

Preprints

1. Boundary slopes of some non-Montesinos knots, 2014. arXiv

2. (w. Dionne Ibarra, Dan Mathews & Lecheng Su) Lambda lengths in the figure eight knot complement, 2024.  arXiv

3. Coiled surfaces and the strong slope conjecture, in preparation

4. The structure of generalised alternating link projections, in preparation

5. (w. Hyam Rubinstein) Weakly generalised alternating links, in preparation

Thesis

Surface-alternating knots and links, University of Melbourne, 2015. link

Talks and slides

1. Geography of spanning surfaces, 2021

2. Alternating genera of torus knots, 2019

3. Exceptional fillings of weakly generalised alternating links, 2018

4. Quasifuchsian checkerboard surfaces, 2016

5. Uniformly twisted knots and the slope conjectures, 2016

6. A characterisation of alternating knot exteriors, 2014

7. Boundary slopes of generalised alternating knots, 2013