People
Moon Duchin Associate Professor
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
BromfieldPearson
Room 113
Medford, MA 02155
Email @tufts.edu:
moon.duchin
Phone: 6176275970
Personal site
Expertise:
Geometry of groups and surfaces
Research:
My research is in geometric group theory and geometric topology,
with tools from dynamics. I look at the metric geometry of groups
and surfaces, often by zooming out to the large scale picture. I've
been thinking about ways to do coarse geometry more "finely" by
paying attention to properties that are destroyed by usual notions
of largescale equivalence.
Lately I am drawn to geometric counting problems, in the vein of the
classic Gauss circle problem, which asks how many integer points in
the plane are contained in a disk of radius r. If instead of a
circle you count points inside dilates of a polygon or polytope,
then you are led to Ehrhart theory, a rich subject with connections
to convex geometry and algebraic geometry. You can set up a version
of this counting problem for arbitrary metric spaces and arbitrary
lattices of points, or devise a version for finitely generated
groups. Solutions to these counting problems allow you to make very
precise calculations in geometric probability. I've also been
thinking about filling invariants, geometry "at infinity," and the
dynamics of random transformations.
My graduate training was in lowdimensional topology and ergodic
theory, focusing on an area called Teichmüller theory, where the
object of interest is a parameter space for geometric structures on
surfaces. Teichmüller space is a model space for the action of a
discrete group called the mapping class group, which is generated by
Dehn twists about curves on a surface. Other objects I look at
include rightangled Artin groups and the CAT(0) cube complexes they
act on; the real and discrete Heisenberg groups; billiard tables as
dynamical systems; and the metrics that arise in convex geometry.
I have also worked and lectured on issues in the history,
philosophy, and cultural studies of math and science, such as the
role of intuition and the nature and impact of ideas about genius.
I'm involved in a range of educational projects in mathematics: I am
a veteran visitor at the Canada/USA Mathcamp for talented high
school students; I have worked with middle school teachers in
Chicago Public Schools, developed inquirybased coursework for
future elementary school teachers at the University of Michigan, and
briefly partnered with the Poincaré Institute for Mathematics Education at
Tufts.
