Dongping Zhuang
Stevenson Center 1426
Department of Mathematics
Vanderbilt University
Nashville, TN 37240
dongping.zhuang at vanderbilt dot edu
Curriculum Vitae
available in pdf
Research Interests
Geometric group theory, including dynamics, geometry and rigidity
of groups
and their applications to low dimensional topology and
dynamical systems.
Papers
- Irrational Stable Commutator Length in Finitely Presented Groups pdf
Journal of Modern Dynamics(JMD), Volume 2, No.3, 497-505, 2008
- Large Scale Geometry of Commutator Subgroups pdf
(with Danny Calegari) Algebr. Geom. Topol. 8 (2008), 2131-2146 (electronic).
- Thesis: A Geometric Study of Commutator Subgroups (Defended May 12, 2009)
Work in progress
- Large scale geometry of spaces with bi-invariant metrics
- We study the Cayley graph of the commutator subgroup of a hyperbolic group,
with commutator length as the metric.
We show that for any non-elementary hyperbolic
group, there exists a quasi-embedded Z^n in this graph for any n.
Thus the Cayley
graph is not word-hyperbolic, and it has infinite asymptotic dimension.
See section 5.4.3 of my thesis.
- Let G be the group of area-preserving homeomorphisms of the unit 2-disc that
are the identity near the boundary.
We normalize the disc to have area 1, and
consider the fragmentation norm with size s, 0 < s < 1. It is known that G
with this bi-invariant metric is unbounded. In fact, we can show that there exists
a quasi-isometrical embedding
from Z^n into G for any n. Thus G, with the
fragmentation metric, has infinite asymtotic dimension.
- Both of the results can be regarded as the geometric applications of quasimorphisms.
Teaching
Links