Research Area: Geometric topology and Knot theory.

Publications:
  1. A note on quasi-alternating Montesinos links (joint with Philip Ording), accepted for publication in J. Knot Theory and its Ramifications
  2. A survey on the Turaev genus of knots. (joint with Ilya Kofman), Acta Mathematica Vietnamica 39 (2014), no. 4, 497-514.
  3. The 500 simplest hyperbolic knots. (joint with Ilya Kofman and Tim Mullen), J. Knot Theory and its Ramifications, 23 (2014), no. 12, 1450055[1-34].
  4. On the tail of Jones polynomials of closed braids with a full twist (joint with Ilya Kofman), Proceedings of the American Mathematical Society, 141 (2013) 2557-2567.
  5. Volume bounds for generalized twisted torus links (joint with Dave Futer, Ilya Kofman, Walter Neumann and Jessica Purcell), Mathematical Research Letters 18 (2011), no. 6, 1097-1120.
  6. Quasi-tree expansion for the Bollobas-Riordan-Tutte polynomial (joint with Ilya Kofman and Neal Stoltzfus), Bulletin of the London Mathematical Society , (2011) 43(5): 972-984.
  7. Spanning Trees and Khovanov Homology (joint with Ilya Kofman), Proceedings of the American Mathematical Society 137 (2009), no. 6, 2157-2167.
  8. Twisting quasi-alternating links (joint with Ilya Kofman),   Proceedings of the American Mathematical Society 137 (2009), no. 7, 2451 - 2458.
  9. On mutation and Khovanov homology (joint with Ilya Kofman), Communications in Contemporary Mathematics 10 (2008), 973-992. (Special issue in memory of Xiao-Song Lin).
  10. Graphs on surfaces and Khovanov homology (joint with Ilya Kofman and Neal Stoltzfus), Algebraic and Geometric Topology 7 (2007), 1531-1540.
  11. Exceptional regions and associated exceptional hyperbolic 3-manifolds(joint with Jacob Lewis, Max Lipyanskiy, Scott Meltzer and Alan Reid),Experimental Mathematics 16 (2007), no. 1, 107- 118.
  12. On links with cyclotomic Jones polynomials  (joint with Ilya Kofman), Algebraic and Geometric Topology 6 (2006), 1655-1668.
  13. On the Mahler measure of Jones polynomials under twisting(joint with Ilya Kofman),  Algebraic and Geometric Topology 5 (2005), no. 1, 1-22.  
  14. The next simplest hyperbolic knots(joint with Ilya Kofman and Eric Patterson), J. Knot Theory Ramifications 13(2004), no. 7, 965-987.
  15. Classification of surfaces via Morse theory (joint with Ajit Kumar and S. Kumaresan), Expositiones Mathemathicae , 18 (2000) no. 1, 37 -73.

Preprints:
  1. Geometrically and diagrammatically maximal knots (joint with Ilya Kofman and Jessica Purcell), Preprint.
  2. Volume bounds for weaving knots (joint with Ilya Kofman and Jessica Purcell), Preprint.
  3. Quantum density spectra for knots (joint with Ilya Kofman and Jessica Purcell), Preprint.
  4. A-polynomial and Bloch invariants of hyperbolic 3-manifolds Preprint.

Books:
  1. Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory
    A. Champanerkar, O. Dasbach, E. Kalfagianni, I. Kofman, W. Neumann and N.Stoltzfus, editors, Contemporary Mathematics , Volume 541, American Mathematical Society (2011).