Anastasiia's webpage

Peer-Reviewed Publications and Preprints

An alternative approach to hyperbolic structures on link complements (with M. Thistlethwaite), submitted, pdf at arXiv.org

An alternative method is described for determining the hyperbolic structure on a link complement, and some of its simple consequences are examined. The method is based on ideal polygons bounding the regions of a diagram of the link rather than decomposition of the complement into ideal tetrahedra.

Decomposition Of Cellular Balleans (with I. Protasov), Topol. Proc. 36 (2010), pdf;

We consider groups as coarse structures (equivalently, as balleans), and investigate the question of classification of uncountable groups up to coarse equivalence. We prove that any two uncountable groups of regular cardinality are coarsely equivalent.

Asymptotic Rays (with O. Kuchaiev), Int. J. of Pure Appl. Math. 56, no. 3 (2009), pdf

We consider graphs as coarse structures (equivalently, as balleans), and give the necessary and sufficient conditions for a tree to be coarsely equivalent to a ray (i.e. to a graph where the valence of every vertex is 2).

Volume of 2-bridged links, in preparation

We obtain formulas that allow one to calculate hyperbolic and complex volume of a hyperbolic 2-bridged link directly from its diagram.

Published Conference Proceedings

Cellular Balleans Decomposable into Direct Products, Proc. of 4th Summer School in Alg. and Top., Lviv - Kozyova, Ukraine (2006), 162-165

Asymptotic Rays, Proc. of 3rd Summer School in Alg. and Top., Lviv - Kozyova, Ukraine (2005), 140-141

Around Grasshopper Lemma, Proc. of 2nd Summer School in Alg. and Top., Lviv - Dolyna, Ukraine (2004), 19-20

Recent and Forthcoming Talks (for the full list see CV)

University of Virginia geometry seminar, scheduled invited talk, 01/2012

AWM workshop, poster presentation, 01/2012 (poster)

Knots in Washington XXXIII, contributed talk An alternative approach to hyperbolic structures on link complements, 12/2011

Brigham Young University topology seminar, 11/2011, invited talk An alternative approach to hyperbolic structures on link complements

University of Texas, Austin, topology seminar, 10/2011, invited talk Hyperbolic structures on link complements (50 min presentation)

Columbia University geometric topology seminar, New York, 09/2011, invited talk Hyperbolic knot and link complements (1hr presentation)

AMS sectional meeting at Wake Forest University, 09/2011, contributed talk Links and hyperbolic geometry (short presentation, accesible to non-topologists)

Geometric Topology of Knots Workshop, Pisa, Italy, 05/2011, invited talk An alternative approach to hyperbolic structures on link complements

AMS Annual Meeting, New Orleans, 01/2011, contributed talk Investigating hyperbolic link complements

University of Tennessee topology seminar, Knoxville, 02/2011, series of talks about hyperbolic links

12th Chico Topology Conference, 06/2010, research talk Hyperbolic structures on alternating link complements

University of Tennessee, 04/2009, research talk The tilt formula (1 hr presentation)

Selected Honors and Support (for the full list see CV)

AMS Travel Grants, 01/2012 and 10/2011

AWM Travel Grant, 01/2012

UTK Graduate Travel Award, 05/2011

Invited speaker of Geometric Topology of Knots workshop, Pisa, Italy, 05/2011

UTK College of Arts and Sciences award, 01/2011

UTK Science Alliance Fellowship, 2006-2008, 2009-2011

1st place in Microsoft competition, Software design category, Ukraine, 2006 (project Footstep)

Presidential grant funding an undergraduate degree, Ukraine, 2001-2005 (less than 100 grants given annually to exceptional High School students from all disciplines in Ukraine)

Annual winner of All-Ukrainian Mathematical Olympiad, 1997-2001