Andrew Przeworski's Homepage

I'm a Visiting Assistant Professor in the math department at Marshall University. 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 121 (Sections 209 and 217), and Math 203 (Sections 206 and 207).

Publications

• 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
  

How to reach me

Office: SH 743D
Phone (office): 304-696-3443
E-mail: przeworski@marshall.edu