Research Area: Geometric topology and Knot theory.

Publications:
  1. Mahler Measure and the Vol-Det Conjecture (joint with Ilya Kofman and Matilde Lalin), to appear in J. London Mathematical Society .
  2. Geometry of biperiodic alternating links (joint with Ilya Kofman and Jessica Purcell), to appear in J. London Mathematical Society .
  3. Geometrically and diagrammatically maximal knots (joint with Ilya Kofman and Jessica Purcell), J. London Mathematical Society Volume 94, Issue 3, December 2016, Pages: 883-908.
  4. Volume bounds for weaving knots (joint with Ilya Kofman and Jessica Purcell), Algebraic & Geometric Topology 16 (2016) 3301-3323.
  5. Determinant density and biperiodic alternating links (joint with Ilya Kofman), New York J. Math. 22 (2016) 891-906.
  6. Density spectra for knots (joint with Ilya Kofman and Jessica Purcell), J. Knot Theory and its Ramifications, Vol. 25 (2016), no. 3, 1640001 (2016) [1-11].
  7. A note on quasi-alternating Montesinos links (joint with Philip Ording), J. Knot Theory and its Ramifications, Vol. 24 (2015), no. 9, 1550048 [1-15].
  8. A survey on the Turaev genus of knots. (joint with Ilya Kofman), Acta Mathematica Vietnamica 39 (2014), no. 4, 497-514.
  9. 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].
  10. 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.
  11. 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.
  12. 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.
  13. Spanning Trees and Khovanov Homology (joint with Ilya Kofman), Proceedings of the American Mathematical Society 137 (2009), no. 6, 2157-2167.
  14. Twisting quasi-alternating links (joint with Ilya Kofman),   Proceedings of the American Mathematical Society 137 (2009), no. 7, 2451 - 2458.
  15. 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).
  16. Graphs on surfaces and Khovanov homology (joint with Ilya Kofman and Neal Stoltzfus), Algebraic and Geometric Topology 7 (2007), 1531-1540.
  17. 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.
  18. On links with cyclotomic Jones polynomials  (joint with Ilya Kofman), Algebraic and Geometric Topology 6 (2006), 1655-1668.
  19. On the Mahler measure of Jones polynomials under twisting(joint with Ilya Kofman),  Algebraic and Geometric Topology 5 (2005), no. 1, 1-22.  
  20. The next simplest hyperbolic knots(joint with Ilya Kofman and Eric Patterson), J. Knot Theory Ramifications 13(2004), no. 7, 965-987.
  21. Classification of surfaces via Morse theory (joint with Ajit Kumar and S. Kumaresan), Expositiones Mathemathicae , 18 (2000) no. 1, 37 -73.

Preprints:
  1. Examples of homological torsion and volume growth (joint with Ilya Kofman), Preprint.
  2. 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).
PhD students: