Research

I spend most of my time attempting to answer questions concerning the geometry of 3-manifolds algorithmically.

In prepartaion

  1. (with Christine Lee) Normal Surfaces and Colored Jones Slopes
  2. (with Mingming Zhang) Limits of Mahler measures of Alexander polynomials.
  3. (with William Jaco) Essential surfaces with boundary in general ideal triangulations.

Preprints

  1. Multivariable Alexander polynomials of twisted torus links via Dehn surgery. (arxiv)
  2. Ideal triangulations and once-punctured surface bundles. (submitted to Alg. & Geo. Top.) (arxiv)

Publications

  1. (with William Jaco and Hyam Rubinstein) Efficient triangulations and boundary slopes. Topology and Its Applications vol. 297 (2021) (article) (arxiv)

Notes

If you are a student interested in working on a project, these notes will give an idea about some projects I have had on my mind.
  1. Octaheral triangulations: I have been using these for all types of 3-manifodl computations.
  2. Normal Surfaces in 3-skeleta: I have many thoughts on normal surfaces embedded in higher dimension triangulations.
  3. Crushing Essential Surfaces It would be nice to build the complete picture of what happens to surfaces under Jaco-Rubinsteins crushing map.