People
Michael BenZvi Norbert Wiener Assistant Professor
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
BromfieldPearson
Medford, MA 02155
Email @tufts.edu:
michael.ben_zvi
Personal website
Expertise:
Geometric group theory
Research:
Geometric group theory explores the rich connection between
algebraic and geometric properties of a group. This interplay comes
in two different ways. The first is viewing a group, G, as
a geometric object itself by fixing a generating set. This endows
G with the word metric, allowing us to make sense of
distance within the group. We can then try to understand algebraic
properties of the group through studying the geometry of G
with the word metric. Fixing a generating set also lets us draw a
picture of G in the form of its Cayley graph and G
naturally acts in a nice way on its Cayley graph. This gives rise to
the second way of studying the relationship between algebra and
geometry: through spaces on which the group acts geometrically. It
turns out that when a group acts geometrically on a space, these two
objects are coarsely equivalent, letting us make connections between
the algebraic properties of the group and the geometric properties
of the space.
A major area of study within geometric group theory has been the
study of hyperbolic groups. These are groups which act on spaces
with negative curvature and they have lots of nice algebraic and
geometric properties. A generalization of hyperbolic groups is
CAT(0) groups. These are groups which act on spaces with
nonpositive curvature. My research has been on understanding when
certain properties of hyperbolic groups are also properties of
CAT(0) groups. In particular, my focus has been on understanding the
boundaries, the space at infinity, of such groups.
