EMSW21-RTG: Enhancing the Research Workforce in Algebraic Geometry and its Boundaries in the Twenty-First Century

该项目在密歇根大学建立了代数几何及其边界领域的研究培训计划。目标学员为刚毕业的博士和高级研究生。该项目由五位高级教员负责，他们代表了代数几何领域当前广泛的研究趋势，并与密歇根大学相关领域的另外14位高级教员进行了磋商。活动包括创新研讨会结构，为学员提供广泛接触代数几何（广义解释）的各种基础和研究水平主题的机会；一所年度学校（也向密歇根州以外的年轻研究人员开放），涵盖由密歇根州以外的著名研究人员教授的当前重要研究课题；博士后研究人员有机会在资深教师的指导下设计和领导REU项目；为高级研究生和博士后提供发展技术演讲和写作技能的机会；并为博士后和高级研究生提供许多机会，在数学研究生涯的各个方面接受指导。代数几何是当今数学中最核心和最活跃的分支之一，与其他数学和科学分支的联系日益重要。代数几何也是数学在技术和政府中的许多应用的基础，包括编码理论（给我们带来，例如，光盘）和样条理论（给我们带来计算机辅助设计和某些医疗应用和好莱坞电影必不可少的计算机图形），以及由国家安全局开创的国家安全的重要问题。20世纪末代数几何的爆炸性增长，使这一领域的研究成为一个非常激动人心的时期，但也使年轻的研究人员难以起步。该项目将增加在代数几何及其边界领域受过广泛训练的研究人员的流动，从而加强21世纪这些重要数学领域的培训基础设施和研究人员队伍。

The project establishes a research training program in algebraic geometryand its boundary areas at the University of Michigan. Target trainees arerecent PhDs and advanced graduate students. The project is run by fivesenior faculty members representing a wide swath of current researchtrends in algebraic geometry, in consultation with an additional 14 seniorfaculty at Michigan in related areas. Activities include innovations inseminar structure offering trainees broad exposure to a wide variety ofbasic and research level topics in algebraic geometry (broadly construed);an annual school (open also to young researchers outside Michigan)covering a research topic of current importance taught by a prominentresearcher from outside Michigan; opportunities for post-doctoralresearchers to design and lead REU projects under the mentorship of asenior faculty member; opportunities for advanced graduate students andpost-docs to develop their technical lecturing and writing skills; andnumerous opportunities for post-docs and advanced graduate students toreceive mentoring on all aspects of a research career in mathematics.Algebraic geometry is one of the most central and active branches ofmathematics today, with increasingly important connections to otherbranches of mathematics and science. Algebraic geometry also underliesmany applications of mathematics to technology and government, includingcoding theory (bringing us, for example, the compact disc) and splinetheory (bringing us computer aided design and the computer graphicsessential to certain medical applications and Hollywood movies), as wellas important issues of national security pioneered by the NationalSecurity Agency. The explosive growth of algebraic geometry at the end ofthe twentieth century has made this a very exciting time to begin researchin the field, but it has also made it difficult for young researchers toget started. This project will increase the flow of broadly trainedresearchers in algebraic geometry and its boundary areas, thereforeenhancing the training infrastructure and the research workforce in thesevital areas of mathematics in the twenty-first century.