I'm an Associate Professor in the math department at the College of Charleston. My area of interest is the geometry and topology of hyperbolic 3-manifolds, in particular as these topics relate to packing problems in hyperbolic space. Right now, I'm working on packings of tubes. This semester, I'll be teaching Math 120 and Math 221.

- An Upper Bound On Density For Packings Of Collars About Hyperplanes In H
^{n}(PDF, Journal version) : Proves a version of Rogers' Lemma for packings of collars about hyperplanes in hyperbolic space. This produces an upper bound on density which is sometimes sharp (depending on the radius of the collars). Geom. Dedicata**163**No. 1, April 2013, 193-213. - Delaunay Cells for Arrangements of Flats in Hyperbolic Space
(PDF, Journal version) : Constructs Delaunay cells dual to the Voronoi tessellation.
Under certain circumstances, shows that the Delaunay cells give something resembling a tiling of
hyperbolic space. (The title of this paper has changed. The word "flats" used to be "hyperplanes") Pacific J. Math
**258**No. 1 July 2012, 223-256. - Packing disks on a torus (
dvi+ps,
Postscript,
PDF file, Journal version):
In questions concerning volumes of tubes embedded in hyperbolic manfolds, one often needs to
know the densest way to pack nonoverlapping congruent disks on a cylinder (while restricting to
a very specific type of packing).
By lifting to the euclidean plane, we are asking for the
densest way to pack two identical lattice's worth of disks. This depends on the ratio of the disk
radius to the cylinder circumference. We identify the densest packing for any given ratio. This paper was formerly titled "Double lattice packings in the Euclidean plane". Discrete Comput. Geom.
**35**(2006), no. 1, 159--174. - A universal upper bound on density of tube packings in hyperbolic space (
dvi+ps,
Postscript,
PDF file, Journal version):
Hyperbolizes a Euclidean result to produce
an upper bound on density of tube packings in hyperbolic space. When combined
with two earlier density results, this produces a universal upper bound on
density. J. Differential Geom.
**72**(2006), no. 1, 113--127. - Balls in hyperbolic 3-manifolds (dvi, Postscript, PDF): Shows that any closed orientable hyperbolic 3-manifold contains a ball of radius 0.17. Houston J. Math.
**31**(2005), no. 1, 161--171 - Density of tube packings in hyperbolic space(dvi+eps, Postscript, PDF, Journal version): Establishes an upper bound on the density of tube packings in hyperbolic space. Also improves estimates on volume and geodesic length for small volume hyperbolic 3-manifolds. Pacific J. Math.
**214**(2004) no. 1, 127-144 - Tubes in hyperbolic 3-manifolds (dvi,
Postscript, PDF):
Shows that any closed orientable
hyperbolic 3-manifold has volume at least 0.27. Top. and Appl.
**128**/2-3 103-122 - Volumes of hyperbolic 3-manifolds of betti number at least
3 (dvi, Postscript, PDF):
Shows that any closed orientable hyperbolic 3-manifold with betti
number at least 3 has volume at least 1.015.
Bull. London Math. Soc.
**34**(2002) no. 3, 359-360 - Cones embedded in hyperbolic
manifolds (dvi with eps, Postscript, PDF, Journal version):
Establishes a lower bound on the volume outside of a
maximal tube. This has a number of applications, one of which is a
lower bound of 0.09 on the length of the shortest geodesic in the
smallest hyperbolic 3-manifold.
J. Differential Geom.
**58**(2001), no. 2, 219-232

- A Duality Property Of Delaunay Faces For Line Arrangements In H
^{3}(PDF, Journal version) : Three distinct lines in H^{3}determine a Delaunay face. The pairwise common perpendiculars to those three lines also bound the face. We prove that the Delaunay face of the pairwise common perpendiculars is the same as for the original three lines. To appear in Publi. Math. Debrecen

Office: RSS 335

Phone (office): 843-953-5729

E-mail: przeworskia@cofc.edu