# Research

**Publications and Preprints**(all peer-reviewed; authors in alphabetical order; for works in preparation see Annotated Publication List above).

*Standard position for surfaces in link complements in arbitrary 3-manifolds*, with J. Purcell, preprint, pending revisions in Algebraic and Geometric Topology, ArXiv

*Random meander model for links*, with N. Owad, preprint, pending revisions in Discrete & Computational Geometry, ArXiv

*NP-hard problems naturally arising in knot theory*, with D. Koenig, Transactions of American Mathematical Society Ser. B 8 (2021), 420-441, ArXiv

*Unlinking, splitting, and some other NP-hard problems in knot theory*, with D. Koenig, Proceedings of Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM (2021), 1496–1507

*Tangle decompositions of alternating link complements,*with J. Hass and A. Thompson, llinois Journal of Mathematics 65 (2021), no. 3, 533–545, ArXiv

*The number of Seifert surfaces of fixed genus is polynomial in the crossing number for an alternating link,*with J. Hass and A. Thompson, Indiana University Mathematics Journal 70 (2021), no. 2, 525-534 , ArXiv

*Simplicial volume of links from link diagrams*, with O. Dasbach, Mathematical Proceedings of Cambridge Philosophical Society 166 (2019), no. 1, 75-81 , Arxiv

*Determining isotopy classes of crossing arcs in alternating links*, Asian Journal of Mathematics Vol. 22, No. 6 (2018), 1005-1024,

*ArXiv*

*The number of incompressible surfaces in an alternating link complement,*with J. Hass and A. Thompson, International Mathematics Research Notices 6 (2017), 1611-1622, ArXiv

*Intercusp parameters and the invariant trace field,*with W. Neumann, Proceedings of the American Mathematical Society 14 (2016), No. 2, 887-896,ArXiv

*A refined upper bound for the hyperbolic volume of alternating links and the colored Jones polynomial,*with O. Dasbach, Mathematical Research Letters 22 (2015), No. 4, 1047-1060, ArXiv

*Exact volume of hyperbolic 2-bridge links*, Communications in Analysis and Geometry 22 (2014), No. 5, 881-896, ArXiv

*An alternative approach to hyperbolic structures on link complements,*with M. Thistlethwaite, Algebraic & Geometric Topology 14 (2014), 1307-1337, ArXiv

*Hyperbolic Structures from Link Diagrams*, Ph.D. Thesis, Unversity of Tennessee (2012),

*Decomposition Of Cellular Balleans,*with I. V. Protasov, Topology Proceedings 36 (2010), 77-83, ArXiv

*Asymptotic Rays,*with O. Kuchaiev, International Journal of Pure Appl. Math. 56, no. 3 (2009), 353-358, ArXiv

**Some Software**