Mathematical Sciences REU Site: Computationalc Geometry Algebraic Geometry

9415268 Laubenbacher研究员组织了一个为期五天的关于Groebner基和凸多面体的研讨会，以Bernd Sturmfels教授的十个系列讲座为特色，描述了关于环面理想的Groebner基的一些核心结果及其在整数规划和统计问题中的应用。除了这些讲课外，还有一份同时提交的论文。多项式方程在代数几何和交换代数中占有重要地位。此外，许多科学、经济和工程问题可以用多项式方程建模，多项式出现在计算统计、整数规划和各种其他优化问题中。Groebner基理论为分析这类方程的许多算法提供了基础。因此，这一理论不仅在基础研究中发挥着重要作用，而且在解决战略利益问题上也具有重要意义。这一理论越来越多地成为美国大学标准课程的一部分。因此，会议的主题引起了几个学科的学生、教师和研究人员的兴趣，包括数学、工程、计算机科学和运筹学。

9415268 Laubenbacher The investigator organizes a five-day symposium on Groebner bases and convex polytopes, featuring a series of ten lectures by Professor Bernd Sturmfels describing some of the central results about Groebner bases of toric ideals and their application to problems in integer programming and statistics. These lectures are complemented by a concurrent contributed paper session. Polynomial equations are important in algebraic geometry and commutative algebra. Moreover, many scientific, economic and engineering problems can be modeled by polynomial equations, and polynomials arise in computational statistics, integer programming, and a variety of other optimization problems. The theory of Groebner bases provides the foundation for many algorithms used in the analysis of such equations. So the theory plays a significant role not just in basic research but also in the solution of problems of strategic interest. Increasingly, this theory is becoming part of the standard curriculum at U.S. universities. Thus, the subject the conference is of interest to students, teachers and researchers in several disciplines, including mathematics, engineering, computer science, and operations research.