Department of Mathematics
503 Boston Avenue
Medford, MA 02155
Ph.D. Brandeis University
Combinatorial and geometric group theory
I study algebra, that is, the study of operations such as addition
but in an abstract setting. My training, however, was originally in
geometry, in particular in the area of knots (but of things like
spheres knotted in 4 dimensions). It turns out that one can
associate to these knots a group that tells you a lot about the
knot. So I started looking at the group and pretty much forgot about
the knot. In recent years a happy marriage between geometry and
algebra has taken place and one can look at these abstract groups as
genuinely geometric objects, with things like geodesics and
triangles. So far, I have written one paper on this new topic, I am
writing a second and hope to complete a third (on automata groups)
with a former colleague here at Tufts. I like the fact that I can
join my two interests in one single topic. This is in fact, a very
"hot" topic, meaning it is easy to get scooped (as we partially were
on the automata group).
Publications (since 1995):
- (with D. Benardete and Z. Nitecki) Braids and the
Nielsen-Thurston classification. J. Knot Theory 4 (1995),
- (with M. Arkowitz) Comultiplications on monoids. Int. J.
Math. and Math. Sci. 20 (1997), 803-812
- (with S. Krstic) Normal forms for basis-conjugating
automorphisms of a free group. Int. J. Algebra and Comp. 8
- (with M. Arkowitz) Comultiplications on free groups and
wedges of circles. Trans. A.M.S. 350 (1998), 1663-1680.
- (with M. Arkowitz) Coactions of groups. Proc. Royal Math.
Soc. Edin. 131A (2001), 225-239.
- (with M. Arkowitz) Equalizers and coactions of groups. Fund.
Math. 171 (2002), 225-239.
- (with J. Burillo, S. Krstic and Z. Nitecki) Crossing
matrices and Thurston's normal form for braids. Topology and
Appl. 118 (2002), 293-308.
- (with A. Kaul) Automorphisms of right-angled Coxeter groups.
Int. J. Math. and Math. Sci. (to appear)
- (with A. Piggott) Rigidity of graph products of abelian
groups. J. Australian Math. Soc. (to appear)
- (with A. Piggott and K. Ruane) Automorphisms of graph
products of abelian groups. (submitted)
- (with L. Corredor) The centralizer theorem for graph products of abelian groups. (preprint)