Here is a list of my publications and preprints (yet to be published work has its arxiv listing).
A list of this work with short descriptions, questions, and slides is available here.
arxiv google scholar
In preparation.
  1. (with Ken Baker and Joan Licata) Unifying unexpected exceptional Dehn fillings.


Preprints.
  1. (with Stavros Garoufalidis, Craig Hodgson, and Hyam Rubinstein) The 3D-index and normal surfaces arxiv
  2. (appendix to Ken Baker's paper) The Poincare homology sphere, lens space surgeries, and some knots with tunnel number two arxiv.
  3. (with Jessica Purcell) Geometry of planar surfaces and exceptional fillings.arxiv
  4. (with Nathan Sunukjian) Surfaces in 4-manifolds: smooth isotopy arxiv


Publications (in print and accepted).
  1. (with Genevieve Walsh) The big Dehn surgery graph and the link of \(S^3.\) Proc. AMS, Ser B (open access) \(\dagger\) (Also, see ancillary files.)
  2. (with Nathan Dunfield and Joan Licata) Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling, arxiv (Note: see ancillary files for the code.) Math Research Letters, Vol. 22, No. 6 (2015) 1679-1698.
  3. (with Kazuhiro Ichihara, Masahide Kashiwagi, Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu) Verified computations for hyperbolic 3-manifolds. arxiv code Exp. Math. 25.1 (2016): 66-78.
  4. (with Ken Baker and Brandy Guntel Doleshal) On manifolds with multiple cyclic fillings, and generalized Berge knots. Boletin de la Sociedad Matematica Mexicana, 20(2) 2014 pp 401-447. arxiv
  5. On knot complements that decompose into regular ideal dodecahedra, Geom. Ded. Vol 173(1) (2014) arxiv The computation written as a magma file is here.
  6. Small knot complements, exceptional surgeries and hidden symmetries, Alg. & Geo. Top. Vol 14 (2014),pdf arxiv
  7. Commensurability classes containing three knot complements, Alg. & Geo. Top, Vol 10 (2010) pdf
\(\dagger\) Detailed instructions on how to input the Kanenobu tangle into Damian Heard's ORB, can be found here.


Some of this work (1 & 2) made it into my thesis, which was advised by Alan Reid.

Finally, I had the wonderful oppurtunity to be apart of the SMALL program as an undergraduate and work with Frank Morgan.

Here is a publication that resulted from that project:

(with J. Corneli et al.) Double Bubbles in \(S^3\) and \(H^3\), J. of Geo. Anal. Vol 17, No 2 (2007) pdf ****Code available in the arxiv version


Supervised Research


(co-supervised with Craig Hodgson) Blake Dadd and Alex Duan, "Constructing infinitely many geometric triangulations of the figure eight knot complement". To appear in Proc. AMS pdf arxiv

(co-supervised with Craig Hodgson) Emma Kong and Curtis Mustgrave-Evans. "Maximal equal area cusp packings of punctured spheres".



Curriculum vita (pdf). Updated July 2016.