US Participation in Workshop: Enumeration and Bounds in Real Algebraic Geometry

美国参加研讨会：实代数几何中的枚举和界限

• 批准号: 0800253
• 负责人: Frank Sottile
• 金额: $ 1.2万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-04-01 至 2009-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0800253&HistoricalAwards=false
• 关键词: US; Participation; Workshop; Enumeration; Bounds

ABSTRACTPrincipal Investigator: Sottile, Frank J.Proposal Number: DMS - 0800253 Institution: Texas A&M Research Foundation Title: Workshop on Enumeration and Bounds in Real Algebraic GeometryA priori information about the real solutions to a system of polynomial equations is important for the applications of mathematics, which typically only need the real solutions. The current state of knowledge about this problem, particularly counting or bounding the numbers of solutions, will be the focus of a workshop to be held at the Bernoulli Center in the EPFL (Swiss Federal Technological Institute) in Lausanne, Switzerland the week of April 21 to April 25 in 2008. This is embedded within a semester long program at the Bernoulli Center on real and tropical algebraic geometry. This project will fund the participation of scientists from the United States at this workshop.It is notoriously difficult to extract any information about real solutions to equations without first solving them completely by finding all complex solutions. Recent breakthroughs have led to new insights about bounds, both upper and lower for the number of real solutions to some structured systems of polynomial equations. There are also new algorithms for only computing the real solutions. At the same time, a better understanding has arisen about average-case behavior, and other scientists have begun to apply these results. This workshop will be small (about 20 participants) and very focused on current developments and future prospects for this important problem of understanding the real solutions to polynomial equations.

摘要主要研究者：Sottile，Frank J.提案编号：DMS - 0800253机构：德克萨斯A& M研究基金会标题：真实的代数几何中的枚举和边界研讨会关于多项式方程组的真实的解的先验信息对于数学应用是重要的，数学应用通常只需要真实的解。 关于这个问题的知识现状，特别是计算或限制解决方案的数量，将是年在伯努利中心举行的研讨会的重点。 2008年4月21日至4月25日的一周，瑞士洛桑的EPFL（瑞士联邦技术学院）。 这是嵌入在一个学期长的计划在伯努利中心的真实的和热带代数几何。 该项目将资助美国科学家参加这一讲习班。众所周知，如果不先通过找到所有复解来完全解出方程，就很难提取关于方程真实的解的任何信息。 最近的突破导致了新的见解的界限，上限和下限的真实的解决方案的一些结构系统的多项式方程。 也有新的算法只计算真实的解决方案。 与此同时，人们对一般情况下的行为有了更好的理解，其他科学家也开始应用这些结果。 这个讲习班将是小型的（约20名与会者），非常侧重于当前的发展和未来的前景，这一重要问题的理解真实的解决方案多项式方程。