Your student can have a look in "Computational Algebraic Geometry and
Computational Algebra" edited by David Eisenbud and Lorenzo Robbiano
(Symposia Math. XXXIV), for example. There he can find what interests
whom and where.
Among other people, there are Bayer and Stillman (Macaulay), Giovini and
Niesi (CoCoA). The first two in USA, the last two in Italy (Trieste I think).
For CoCoa you can mail to email@example.com . At the same university
in Genova you can contact Lorenzo Robbiano.
I know about other people in France (A. Galligo in Nice, M. Chardin in
You can look also in the MEGA'92 volume (Birkhauser).