A tiling of a surface is a covering of the surface by polygons without
gaps or overlaps such as in the icosahedral
tiling of the sphere. For highly symmetric tilings the geometry of
the tiling is controlled by structure of the symmetry group of the
tiling. The talk gives a quick overview of the link between the tilings
and then lists several problems suitable for undergraduate research. Published
results of one student collaboration for the summer 1997 and 1998
program are given, with a link to a published paper combining their results,
with those of later students and my own results.
Relevant Published paper: Divisible Tilings in the Hyperbolic Plane:
(with Dawn M. Haney, Lori T. McKeough, Brandy M. Smith), New York Journal
of Mathematics 6 (2000), 237-283. (link
to journal, link
to paper)