RTG: Algebra, Geometry, and Topology at UIC

RTG：UIC 的代数、几何和拓扑

• 批准号: 2037569
• 负责人: Izzet Coskun
• 金额: $ 249.98万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2037569&HistoricalAwards=false
• 关键词: RTG; Algebra; Geometry; Topology; UIC

The Research Training Group in Algebra, Geometry, and Topology at the University of Illinois at Chicago (UIC) will conduct a suite of activities spanning educational levels from high school to postdoctoral. Faculty will lead graduate and postdoctoral research in algebraic geometry, commutative algebra, topology, and algebraic topology. Activities will include conferences, learning seminars, and workshops to bridge the gap between coursework and current research. Undergraduate students will be involved in mathematical research through projects in a Mathematical Computing Laboratory and summer research opportunities. Professional development workshops will help students and postdoctoral fellows prepare for success in their future careers. To recruit the next generation of talented students into the mathematical sciences, the project activities will include high school research projects, Sonia Kovalevsky Day workshops, an Undergraduate Mathematics Symposium, and participation in the UIC Math Olympiad Project enrichment program for gifted students in grades 7-12. The program will develop mentoring activities in association with the UIC Emerging Scholars Program and the Association for Women in Mathematics to improve retention and to increase the proportion of female and minority students and postdocs in the mathematical workforce.The field of algebraic geometry is among the most fundamental and active areas of research mathematics. Algebraic geometers study the properties of geometric objects defined by algebraic equations, using tools from algebra, analysis, and topology. Techniques in algebraic geometry have developed into important tools for resolving questions in number theory, complex geometry, string theory in mathematical physics, cryptography, and computer-aided geometric design. This Research Training Group (RTG) project will train undergraduates, graduate students, and postdoctoral fellows in algebraic geometry and the related fields of commutative algebra, topology, and algebraic topology. The RTG activities aim to integrate these young researchers into the mathematical community. It is expected that the students and postdoctoral researchers trained in the program will make significant contributions to these important fields, including the understanding of moduli spaces, birational geometry, characteristic-p techniques, and the topology of three- and four-manifolds.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

伊利诺伊大学芝加哥大学（UIC）的代数，几何学和拓扑的研究培训小组将进行一套跨越高中教育水平的活动。教师将领导代数几何，交换代数，拓扑和代数拓扑的毕业生和博士后研究。活动将包括会议，学习研讨会和研讨会，以弥合课程和当前研究之间的差距。本科生将通过数学计算实验室和夏季研究机会中的项目参与数学研究。专业发展研讨会将帮助学生和博士后研究员为未来的职业做准备。为了招募下一代才华横溢的学生进入数学科学，该项目活动将包括高中研究项目，Sonia Kovalevsky Day研讨会，本科数学研讨会，以及参加7-12岁毕业生的UIC Math Olympiad项目丰富计划。该计划将与UIC新兴学者计划和数学女性协会共同开发指导活动，以改善保留率，并增加数学劳动力中女性和少数族裔学生和博士后的比例。代数几何学领域是研究数学的最基本和活跃领域之一。代数几何体研究代数方程定义的几何对象的性质，使用代数，分析和拓扑的工具。代数几何形状中的技术已发展为重要的工具，用于解决数字理论，复杂几何，数学物理学，密码学和计算机辅助几何设计中的弦理论。该研究培训小组（RTG）项目将培训代数几何学的本科生，研究生和博士后研究员以及交换代数，拓扑和代数拓扑的相关领域。 RTG活动旨在将这些年轻研究人员纳入数学社区。预计在该计划中培训的学生和博士后研究人员将为这些重要领域做出重大贡献，包括对模量空间的理解，生物元素的几何形状，特征P技术以及三个月和四个月的拓扑结构。这项奖项反映了NSF的法定任务，并通过评估了基金会的范围来反映支持者的支持者，并构成了基金会的范围。