Research Assistants: P. Keskar, G. Zhuang
Sponsor: NSF
Our research is in algorithmic algebraic geometry with special emphasis on the following topics:
1. Multi-polynomial resultants
2. Resolution of singularities in characteristic 
3. Galois groups of algebraic curves
Sample open problems in these areas include:
(a) An efficient algorithm for the computation of the multi-polynomial Macaulay resultant.
(b) A constructive desingularization of algebraic varieties of any dimension over fields of characteristic zero.
(c) A desingularization theorem for algebraic varieties of any dimension over fields of nonzero characteristics.
(d) The computation of Galois groups of any algebraic curve.
These open problems now suddenly seem within reach of suitable answers because of wide progress in computational commutative algebra, the easy availability of sophisticated computer algebra programs, and the complete classification of finite simple groups.