Research Area: Geometric topology and Knot theory.
Publications:
 Mahler Measure and the VolDet Conjecture (joint with Ilya Kofman and Matilde Lalin), to appear in J. London Mathematical Society .
 Geometry of biperiodic alternating links (joint with Ilya Kofman and
Jessica Purcell), to appear in J. London Mathematical Society .
 Geometrically and diagrammatically maximal knots (joint with Ilya Kofman and
Jessica Purcell), J. London Mathematical Society Volume 94, Issue 3, December 2016, Pages: 883908.

Volume bounds for weaving knots (joint with Ilya Kofman and
Jessica Purcell),
Algebraic & Geometric Topology 16 (2016) 33013323.
 Determinant density and biperiodic alternating links (joint with Ilya Kofman),
New York J. Math. 22 (2016) 891906.

Density spectra for knots (joint with Ilya Kofman and
Jessica Purcell),
J. Knot Theory and its Ramifications, Vol. 25 (2016), no. 3, 1640001 (2016) [111].
 A note on
quasialternating Montesinos links (joint with Philip Ording),
J. Knot Theory and its Ramifications, Vol. 24 (2015), no. 9, 1550048 [115].

A survey on the Turaev genus of knots.
(joint with Ilya Kofman),
Acta Mathematica Vietnamica 39 (2014), no. 4, 497514.

The 500 simplest hyperbolic knots.
(joint with Ilya Kofman and Tim Mullen),
J. Knot Theory and its Ramifications, 23 (2014), no. 12, 1450055[134].

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) 25572567.
 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, 10971120.
 Quasitree expansion for
the BollobasRiordanTutte polynomial (joint with Ilya Kofman and
Neal Stoltzfus), Bulletin of the London Mathematical Society ,
(2011) 43(5): 972984.
 Spanning Trees
and Khovanov Homology (joint with Ilya
Kofman), Proceedings of the American Mathematical
Society 137 (2009), no. 6, 21572167.
 Twisting
quasialternating links (joint with Ilya Kofman),
Proceedings of the American Mathematical Society 137 (2009),
no. 7, 2451  2458.
 On
mutation and Khovanov homology (joint with Ilya
Kofman), Communications in Contemporary Mathematics
10 (2008), 973992. (Special issue in memory of XiaoSong Lin).
 Graphs on surfaces and
Khovanov homology (joint with Ilya Kofman and Neal
Stoltzfus), Algebraic and Geometric Topology 7 (2007),
15311540.
 Exceptional
regions and associated exceptional hyperbolic 3manifolds(joint
with Jacob Lewis, Max Lipyanskiy, Scott Meltzer and Alan
Reid),Experimental Mathematics 16 (2007), no. 1, 107
118.
 On links with
cyclotomic Jones polynomials (joint with Ilya
Kofman), Algebraic and Geometric Topology 6
(2006), 16551668.
 On the Mahler
measure of Jones polynomials under twisting(joint with Ilya
Kofman), Algebraic and Geometric Topology
5 (2005), no. 1, 122.
 The next simplest
hyperbolic knots(joint with Ilya Kofman and Eric
Patterson), J. Knot Theory Ramifications
13(2004), no. 7, 965987.
 Classification
of surfaces via Morse theory (joint with Ajit Kumar
and S. Kumaresan), Expositiones Mathemathicae , 18 (2000) no. 1, 37
73.
Preprints:
 Examples of homological torsion and volume growth (joint with Ilya Kofman), Preprint.
 Apolynomial and Bloch
invariants of hyperbolic
3manifolds Preprint.
Books:

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: