RTG: Algebra, Geometry, and Topology at UIC

伊利诺伊大学芝加哥分校(UIC)的代数、几何和拓扑学研究培训小组将开展一系列活动，涵盖从高中到博士后的教育水平。教师将领导代数几何、交换代数、拓扑学和代数拓扑学的研究生和博士后研究。活动将包括会议、学习研讨会和研讨会，以弥合课程作业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暑期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他们未来的职业生涯做好准备。为了招收下一代有才华的学生进入数学科学，项目活动将包括高中研究项目、索尼娅·科瓦列夫斯基日工作坊、本科生数学研讨会，以及参加UIC为7-12年级资优学生举办的数学奥林匹克项目丰富计划。该计划将与UIC新兴学者计划和女性数学协会合作开展辅导活动，以提高数学工作者中女性、少数族裔学生和博士后的比例。代数几何领域是数学研究中最基础和最活跃的领域之一。代数几何学家使用代数、分析和拓扑学中的工具，研究由代数方程定义的几何对象的性质。代数几何技术已经发展成为解决数论、复杂几何、数学物理中的弦理论、密码学和计算机辅助几何设计中的问题的重要工具。这个研究培训小组(RTG)项目将培训本科生、研究生和博士后研究员代数几何以及交换代数、拓扑学和代数拓扑学的相关领域。RTG活动的目的是让这些年轻的研究人员融入数学界。预计在该项目中培训的学生和博士后研究人员将在这些重要领域做出重大贡献，包括对模空间、双曲面几何、特征p技巧以及三和四流形的拓扑的理解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.