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.

在代数，几何和拓扑研究训练组在伊利诺伊大学芝加哥（UIC）将进行一套活动，从高中到博士后跨越教育水平。教师将领导代数几何、交换代数、拓扑学和代数拓扑学方面的研究生和博士后研究。活动将包括会议，学习研讨会和讲习班，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的项目和夏季研究机会参与数学研究。专业发展研讨会将帮助学生和博士后研究员为未来职业生涯的成功做好准备。为了招募下一代有才华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日研讨会，本科数学研讨会，以及参加UIC数学奥林匹克项目7-12年级天才学生的丰富计划。该计划将与UIC新兴学者计划和数学女性协会合作开展指导活动，以提高保留率，并增加女性和少数民族学生和博士后在数学劳动力中的比例。代数几何领域是研究数学最基本和最活跃的领域之一。代数几何学家研究由代数方程定义的几何对象的性质，使用代数，分析和拓扑学的工具。代数几何中的技术已经发展成为解决数论、复几何、数学物理中的弦理论、密码学和计算机辅助几何设计中问题的重要工具。这个研究训练小组（RTG）项目将培训本科生，研究生和博士后研究员在代数几何和相关领域的交换代数，拓扑和代数拓扑。RTG的活动旨在将这些年轻的研究人员融入数学界。预计在该计划中培养的学生和博士后研究人员将对这些重要领域做出重大贡献，包括对模空间，双有理几何，特征p技术，以及三个和四个的拓扑结构该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。