I am a graduate student at SUNY-Buffalo
being jointly advised by Johanna Mangahas at my school and Ruth Charney
at Brandeis university. I am mainly interested in geometric group
theory, which studies the interplay between the algebraic structures of
groups and the geometries of the spaces on which they act. The following
theorem is a naive example of the above phenomenon "a group is free if
and only if it admits a free action on some tree". In this theorem, the
geometric property of the tree having no loops, informed the algebraic
property of the group being free and vice versa; this is a theme in
geometric group theory.
I am particularily interested in generalizations of hyperbolicity,
boundaries of groups and CAT(0) cube complexes.