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Mauricio Gutierrez

Mauricio Gutierrez
Contact Info:
Tufts University
Department of Mathematics
503 Boston Avenue
Room 111
Medford, MA 02155

Email @tufts.edu:
Phone: 617-627-2360

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), 293-308.
  • (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 (1998), 631-669.
  • (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)