Travel support for an ICTP workshop

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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.