This might not directly answer your question, but there are a couple of books in the "Lecture Notes in Computer Science" series which are a collection of papers in Applicable/Applied algebra. I am including google books links for these. This might give you an idea of the kind of work taking place in these areas and the people involved. In recent times, I think, there have been a good number commutative algebraists, algebraic geometers, number theorists and combinatorialists working parallel in these areas.

http://books.google.com/books?id=Q61sdIbZdJEC&pg=PA359&dq=applicable+algebra&hl=en&ei=pZjdTOe6JZmJnAffvJyuDw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CD0Q6AEwAw#v=onepage&q=applicable%20algebra&f=false

http://books.google.com/books?id=YVKzPSseyu4C&printsec=frontcover&dq=applicable+algebra&hl=en&ei=pZjdTOe6JZmJnAffvJyuDw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDIQ6AEwAQ#v=onepage&q&f=false

This might not directly answer your question, but there are a couple of books in the "Lecture Notes in Computer Science" series which are a collection of papers in Applicable/Applied algebra. I am including google books links for these. This might give you an idea of the kind of work taking place in these areas and the people involved. In recent times, I think, there have been a good number commutative algebraists, algebraic geometers, number theorists and combinatorialists working parallel in these areas.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 10th International Symposium, AAECC-10, San Juan de Puerto Rico, Puerto Rico, May 10-14, 1993. Proceedings

Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra: 4th International Conference, AAECC-4, Karlsruhe, FRG, September 23-26, 1986. Proceedings