Travel support for an ICTP workshop

这笔赠款将用于资助参加在意大利的里雅斯特国际理论物理中心举行的研讨会和会议的旅费。研讨会和会议的主题是在经典的交换代数，包括研究多重性，希尔伯特函数和积分封闭的理想。第一周将是由四位专家就这些主题提供的一系列短期课程，而第二周是一个研究会议，演讲者来自世界各地。学生和资深教师都将从这次会议中受益。交换代数研究代数方程，如多项式方程和几何之间的关系。这个想法可以追溯到笛卡尔和协调平面的想法，并已被证明是一个强大的工具。许多问题都可以放在解方程组的范围内。例如，线性代数研究线性（一次）方程组。交换代数通过形成由“一般”解组成的代数对象来研究高阶多项式或幂级数方程的解。这些根的代数性质，然后洞察到的几何和代数性质的方程。许多经典问题都可以用这些术语来表述。看似简单的问题，结果却出奇的复杂。例如，有多少多项式沿着平面上的一组点沿着消失的问题等价于理解什么是所谓的希尔伯特函数的理想的多项式沿沿着这些点消失。这些函数用于计算重要的数据。这次会议和研讨会的主题之一是希尔伯特函数及其衍生物的研究。本次研讨会将向年轻的研究人员介绍这一领域的各个方面，涉及该主题的几个部分。会议的一个重要方面是与会者的世界范围;讲习班特别致力于扩大发展中国家的参与。来自美国的研究人员与来自发展中国家的青年研究人员的互动使这一活动成为一个特别的活动。

This grant will support travel to a workshop and conference being held in Trieste, Italy at the International Center for Theoretical Physics. The topics of the workshop and the conference are in classical commutative algebra, including the study of multiplicities, Hilbert functions, and the integral closure of ideals. The first week will be a series of short courses given by four experts on these topics, while the second week is a research conference with speakers from around the world. Both students and senior faculty will benefit from this meeting.Commutative algebra studies the relationship between algebraic equations, such as polynomial equations, and geometry. This idea goes back to Descartes and the idea of coordinatizing the plane, and has proved to be a powerful tool. A wide range of problems can be put into the context of solving systems of equations. For example, linear algebra studies systems of linear (degree one) equations. Commutative algebra studies the solutions of polynomial or power series equations of higher order by forming an algebraic object consisting of the 'generic' solutions. The algebraic properties of these gen then give insight into the geometric and algebraic nature of the equations. Many classical problems can be phrased in these terms. Seemingly simple questions turn out to be surprisingly complicated. For example, questions such as how many polynomials vanish along a set of points in the plane are equivalent to understanding what is called the Hilbert function of the ideal of polynomials vanishing along these points. Such functions are used to count important data.One of the main themes of this conference and workshop is the study of Hilbert functions and their ramifications. This workshop will introduce young researchers to facets of this field which touch several parts of the subject. Am important aspect of the conference is the world-wide scope of the participants; the workshop is especially devoted to broadening participation by developing countries. The interaction of researchers from the United States with young researchers from developing countries make this a special event.