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


Preprints.
  1. Cusp types of quotients of hyperbolic knot complements arxiv
  2. (with Christian Millichap and Will Worden) Symmetries and hidden symmetries of \((\epsilon,d_L)\)-twisted knot complements arxiv
  3. (with Robert Haraway) On the complexity of cusped non-hyperbolicity arxiv


Publications (in print and accepted).
  1. (with Ken Baker and Joan Licata) Jointly primitive knots and surgeries between lens spaces. arxiv. To appear in Communications in Analysis and Geometry.
  2. (with Nathan Sunukjian) Surfaces in 4-manifolds: smooth isotopy arxiv To appear in Algebraic and Geometric Topology
  3. (appendix to Ken Baker's paper) The Poincare homology sphere, lens space surgeries, and some knots with tunnel number two arxiv. To appear in the Pacific Journal of Mathematics
  4. (with Jessica Purcell) Geometry of planar surfaces and exceptional fillings. Bul. of London Math. Society, Vol. 49(2) April 2017, 185-201 pdf arxiv
  5. (with Stavros Garoufalidis, Craig Hodgson, and Hyam Rubinstein) The 3D-index and normal surfaces Illinois J. Math. Volume 60, Number 1 (2016), 289-352.Illinois J. Math. Volume 60, Number 1 (2016), 289-352.arxiv
  6. (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.)
  7. (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.
  8. (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.
  9. (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
  10. 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. I also made a gap version: here which has most of the same functionality.
  11. Small knot complements, exceptional surgeries and hidden symmetries, Alg. & Geo. Top. Vol 14 (2014),pdf arxiv
  12. 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 January 2019.