Mathematical Sciences: Combinatorial Methods in Computational Algebraic Geometry

该奖项支持康奈尔大学Bernd Sturmfels教授在代数几何和组合学方面的研究。Sturmfels博士建议利用凸多面体的组合结构来解决构造代数和代数几何中的问题。他对几何学中出现的组合结构的研究将包括与分级理想相关的高阶拟阵以及它们如何与这些理想的状态多面体相关的研究。这项研究属于组合学的广泛范畴，这是当今数学中最活跃的领域之一。从根本上说，组合学代表着对所有数学活动中的第一项--计数--的系统化。然而，在它的现代发展中，组合数学已经不仅仅是计数，而是利用了各种各样的先进数学技术，尽管它的根源可以追溯到几个世纪前，但由于它在通信和信息技术中的重要性，该领域在过去几十年里有了爆炸性的发展。

This award supports the research in algebraic geometry and combinatorics of Professor Bernd Sturmfels of Cornell University. Dr. Sturmfels has proposed to make use of the combinatorial structure of convex polytopes to attack problems in constructive algebra and algebraic geometry. His research on combinatorial structures arising in geometry will include a study of higher-order matroids associated with graded ideals and how they relate to the state polytopes of these ideals. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. Fundamentally, combinatorics represents a systematization of the very first of all mathematical activities, counting. In its modern development, however, combinatorics has gone beyond just counting to make use of a wide variety of advanced mathematical techniques, and although its roots go back several centuries, the field has had an explosive development in the past few decades because of its importance in communications and information technology.