Research Area: Geometric topology and Knot theory.
Publications:
-
Right-angled polyhedra and alternating links (joint with Ilya Kofman
and Jessica Purcell), Algebraic & Geometric Topology 22-2 (2022), 739-784.
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A volumish theorem for alternating virtual links (joint with Ilya Kofman), New York J. Math. 28 (2022), 337-356.
- Examples of homological torsion and volume growth (joint with Ilya Kofman), Acta Math. Vietnam. 46 (2021), no. 2, 301-308.
- Mahler Measure and the Vol-Det Conjecture (joint with Ilya Kofman and Matilde Lalin), J. London Mathematical Society Volume 99, Issue 3, June 2019, Pages: 872-900.
- Geometry of biperiodic alternating links (joint with Ilya Kofman and
Jessica Purcell), J. London Mathematical Society Volume 99, Issue 3, June 2019, Pages: 807-830.
- 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.
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Volume bounds for weaving knots (joint with Ilya Kofman and
Jessica Purcell),
Algebraic & Geometric Topology 16 (2016) 3301-3323.
- Determinant density and biperiodic alternating links (joint with Ilya Kofman),
New York J. Math. 22 (2016) 891-906.
-
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].
- 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].
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A survey on the Turaev genus of knots.
(joint with Ilya Kofman),
Acta Mathematica Vietnamica 39 (2014), no. 4, 497-514.
-
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].
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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.
- 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.
- 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.
- Spanning Trees
and Khovanov Homology (joint with Ilya
Kofman), Proceedings of the American Mathematical
Society 137 (2009), no. 6, 2157-2167.
- Twisting
quasi-alternating 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), 973-992. (Special issue in memory of Xiao-Song Lin).
- Graphs on surfaces and
Khovanov homology (joint with Ilya Kofman and Neal
Stoltzfus), Algebraic and Geometric Topology 7 (2007),
1531-1540.
- 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.
- On links with
cyclotomic Jones polynomials (joint with Ilya
Kofman), Algebraic and Geometric Topology 6
(2006), 1655-1668.
- On the Mahler
measure of Jones polynomials under twisting(joint with Ilya
Kofman), Algebraic and Geometric Topology
5 (2005), no. 1, 1-22.
- The next simplest
hyperbolic knots(joint with Ilya Kofman and Eric
Patterson), J. Knot Theory Ramifications
13(2004), no. 7, 965-987.
- Classification
of surfaces via Morse theory (joint with Ajit Kumar
and S. Kumaresan), Expositiones Mathemathicae , 18 (2000) no. 1, 37
-73.
Preprints:
- A-polynomial and Bloch
invariants of hyperbolic
3-manifolds Preprint.
Books:
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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:
Masters students:
Anurakti Gupta (2024), thesis done at Indian Institute of Science Education and Research (IISER), Pune.