Neil R Hoffman Office: 165Phone: 61-3-8344-9710 Email: nhoffman(at)ms.unimelb.edu.au Consultation hours: W 2-4, Th 10-11 |

About Me

I am very happy to be at the University of Melbourne, funded by Australian Research Council Discovery Grant DP130103694.(The grant is held by Craig Hodgson, Hyam Rubinstein, and Stephan Tillmann (Sydney).)

For the academic year 2012-2013, I was a guest at the Max Planck Institute for Mathematics in Bonn. Before that, I had the pleasure of

visiting Boston College. Going back any further puts me back in graduate school at the University of Texas where I obtained by PhD.

For more complete information, have a look at my CV (updated January 2016) or here.

to each other. Currently, I am looking at two ways in which this can happen. The first way

is if two manifolds are commensurable ie they share a common finite sheeted cover.

The second way is if two manifolds are related via a Dehn surgery.

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.

12. (with Ken Baker and Joan Licata) Unifying unexpected exceptional Dehn fillings.

11. (with Stavros Garoufalidis, Craig Hodgson, and Hyam Rubinstein) The 3D-index and normal surfaces arxiv

10. (appendix to Ken Baker's paper) The Poincare homology sphere, lens space surgeries, and some knots with tunnel number two arxiv.

9. (with Jessica Purcell) Geometry of planar surfaces and exceptional fillings.arxiv

8. (with Nathan Sunukjian) Surfaces in 4-manifolds: smooth isotopy arxiv

7. (with Genevieve Walsh) The big Dehn surgery graph and the link of $S^3.$ Proc. AMS, Ser B (open access)

6. (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.

5. (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

3. 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.

2. Small knot complements, exceptional surgeries and hidden symmetries, to appear in Alg & Geo. Top, arxiv

1. 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". arxiv

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

Teaching and outreach

Current course: Linear Algebra M10007 (Spring) Course page (requires login).

Classes: MWF 10-11

Consulation hours: W 2-4, Th 10-11

Here is a list of courses I have enjoyed teaching (all seasons local to the hemisphere):

BC Spring 2012:

Linein Math Circle

UT Fall 2009:

Differential Calculus for Natural Science Students (408N)

UT Fall 2007-Spring 2008:

Pre-calculus

TA roles:

Calculus for engineers, Multivariable calculus, Algebraic topology (IBL), Point set topology (IBL)

BC - Boston College - Newton, MA Northern Hemisphere

UT - University of Texas - Austin, TX Northern Hemisphere

IBL - Inquiry based learning aka the Moore method, aka the Socratic method.

Miscellany

In 2011, I was a member of the Infinite Cardinals .It turns out there are good softball math puns out there, for example Tufts' department is proud of their Vector Bases.. (See there are fantastic prizes for getting to the bottom of the page.)