Mathematical Sciences: Algorithmic Algebraic Geometry

计划研究算法代数几何及其在几何建模、有限域上的符号计算和计算群理论中的应用，特别强调以下主题：1。明确的实体模型表示稳健的表面相交3。隐式化和参数化多多项式结果特征p6中奇异点的解析。代数几何是纯数学中一门古老而深刻的学科，涉及几何对象的符号抽象。这是一个目前正在看到各种令人兴奋的应用的领域。

Research is planned in algorithmic algebraic geometry and its applications to geometric modeling, symbolic computations over finite fields, and computational group theory, with special emphasis on the following topics: 1. Unambiguous Solid Model Representations 2. Robust Surface Intersections 3. Implicitization and Parameterization 4. Multi-polynomial Resultants 5. Resolution of Singularities in Characteristic p 6. Galois Groups of Algebraic Curves Algebraic Geometry is a venerable, deep discipline in pure mathematics, involving symbolic abstractions of geometric objects. This is an area that is currently seeing diverse and exciting applications.