Preprints

• Trigonometry of partially truncated hyperbolic triangles and tetrahedra.

Refereed Research Papers

• Dehn surgery and hyperbolic knot complements without hidden symmetries (with Eric Chesebro, Neil Hoffman,
      Christian Millichap, Priyadip Mondal, and Will Worden). International Math Research Notices (2023), no. 6,
      5293--5351. arxiv:2009.14765
• Generic hyperbolic knot complements without hidden symmetries (with Eric Chesebro and Priyadip Mondal).
      To appear, Communications in Analysis and Geometry. arXiv:1910.047212
• The maximal injectivity radius of hyperbolic surfaces with geodesic boundary (with Kim Romanelli).
      Geometriae Dedicata 210 (2021), 103--129. arXiv:1808.05573
• Effective virtual and residual properties of some arithmetic hyperbolic 3-manifolds (with Nicholas Miller and
      Priyam Patel). Transactions of the American Mathematical Society 373 (2020), no. 11, 8219--8257.
      arXiv:1806.02360
• Bounds for several-disk packings of hyperbolic surfaces. arXiv:1701.07770
      Journal of Topology and Analysis 12 (2020), no. 1, 131--167.
• Incompressible solvable representations of surface groups (with Daniel Gomez). arXiv:1704.01007
      Topology and its Applications 229 (2017), 200--212.
• The local maxima of maximal injectivity radius among hyperbolic surfaces. arXiv:1506.08080
      Indiana University Mathematics Journal 66 (2017), no. 4, 1173--1187.
• Bounding the area of a centered dual two-cell below, given lower bounds on its side lengths. arXiv:1506.07978
      New York Journal of Mathematics 23 (2017), 315--349.
• Hidden symmetries via hidden extensions (with Eric Chesebro). arXiv:1501.00726
      Proceedings of the American Mathematical Society 145 (2017), no. 8, 3629--3644.
• The Delaunay tessellation in hyperbolic space. arXiv:1103.4604
    Mathematical Proceedings of the Cambridge Philosophical Society 164 (2018), no. 1, 15--46.
• The geometry of cyclic hyperbolic polygons. arXiv:1101.4971
      Rocky Mountain Journal of Mathematics 46 (2016), no. 3, 801--862.
• Explicit rank bounds for cyclic covers. arXiv:1310.7823
      Algebraic and Geometric Topology 16 (2016), no. 3, 1343--1372.
• The centered dual and the maximal injectivity radius of hyperbolic surfaces. arXiv:1308.5919
      Geometry and Topology 19:2 (2015), 953--1015.
• Rank gradients of infinite cyclic covers of 3-manifolds (with Stefan Friedl and Stefano Vidussi). arXiv:1212.4192
      Michigan Mathematical Journal 63 (2014), no. 1, 65--81.
• Algebraic invariants, mutation, and commensurability of link complements (with Eric Chesebro). arXiv:1202.0765
      Pacific Journal of Mathematics 267 (2014), No. 2, 341--398.
• Some virtually special hyperbolic 3-manifold groups (with Chesebro and Henry Wilton).
      Commentarii Mathematici Helvetici 87 (2012), no. 3, 727--787.
• Cross curvature flow on a negatively curved solid torus (with Dan Knopf and Andrea Young).
      Algebraic and Geometric Topology 10 (2010), no. 1, 343--372.
• On the doubled tetrus. Geometriae Dedicata 144 (2010), 1--23.
• Volume and topology of bounded and closed hyperbolic 3-manifolds (with Peter Shalen).
      Communications in Analysis and Geometry 17 (2009), no. 5, 797--850.
• Incompressible surfaces, hyperbolic volume, Heegaard genus, and homology (with Marc Culler and P. Shalen).
      Comm. Anal. Geom. 17 (2009), no. 2, 155--185.
• Totally geodesic surfaces and homology. Algebr. Geom. Topol. 6 (2006), 1413--1428.
• Surface groups are frequently faithful. (with Autumn Kent) Duke Mathematical Journal 131 (2006), no. 2, 351--362.

Non-refereed

Tessellations of hyperbolic surfaces. arXiv:1103.4604

Rank gradient and the JSJ decomposition, Proceedings of the 26th annual Workshop in Geometric Topology.

Totally geodesic surfaces in hyperbolic 3-manifolds. My U.T. thesis. (My advisor: Alan Reid)