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.
- Cusp types of quotients of hyperbolic knot complements
- (with Christian Millichap and Will Worden) Symmetries and hidden symmetries of \((\epsilon,d_L)\)-twisted knot complements arxiv
- (with Robert Haraway) On the complexity of cusped non-hyperbolicity arxiv
Publications (in print and accepted).
\(\dagger\) Detailed instructions on how to input the Kanenobu tangle into Damian Heard's ORB, can be found here.
- (with Ken Baker and Joan Licata) Jointly primitive knots and surgeries between lens spaces. arxiv. To appear in Communications in Analysis and Geometry.
- (with Nathan Sunukjian) Surfaces in 4-manifolds: smooth isotopy arxiv To appear in Algebraic and Geometric Topology
- (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
- (with Jessica Purcell) Geometry of planar surfaces and exceptional fillings. Bul. of London Math. Society, Vol. 49(2) April 2017, 185-201 pdf arxiv
- (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
- (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.)
- (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.
- (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.
- (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
- 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.
- Small knot complements, exceptional surgeries and hidden symmetries, Alg. & Geo. Top. Vol 14 (2014),pdf arxiv
- Commensurability classes containing three knot complements, Alg. & Geo. Top, Vol 10 (2010) pdf
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
(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".