RTG: Arithmetic, Combinatorics, and Topology of Algebraic Varieties

RTG：代数簇的算术、组合学和拓扑

• 批准号: 2231565
• 负责人: Stefan Patrikis
• 金额: $ 214.23万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-08-15 至 2028-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2231565&HistoricalAwards=false
• 关键词: RTG; Arithmetic; Combinatorics; Topology; Algebraic

The interplay of algebra and geometry is one of the central stories in the history of mathematics, and the modern field of algebraic geometry incorporates many fruitful perspectives accumulated throughout this history. This Research Training Group at Ohio State University will prepare a new generation of researchers in algebraic geometry and related fields, with an emphasis on the subject's wealth of perspectives and consequently deep interactions with other mathematical fields. The program's initiatives are a long-term investment in community-building: in faculty collaboration, in a culture that supports students and postdocs through dense networks of mentoring relationships, and in enhanced efforts to recruit and support members of underrepresented groups. Five thematic years led by experienced faculty will include research training seminars that will ease the transition to research for early-stage PhD students and will broaden the research programs of advanced PhD students and postdocs; conferences at the end of each year will deepen the OSU group's connections to external scholars; and an annual group retreat will consolidate the mentoring network and provide intensive opportunities for collaboration. The project will also support research experiences for undergraduates (REUs), including REUs targeted at Ohio State undergraduates and at students from underrepresented groups across the US. The enhanced faculty coordination behind these programs will lay the foundation for many years of collaboration in research and training, to the benefit of students and scholars at all levels.Fifteen faculty will coordinate the RTG's major initiatives, with students and postdocs playing central roles as both mentors and mentees. The faculty will collaboratively run the 5 thematic years that exhibit arithmetic, combinatorial, and topological perspectives on algebraic varieties. Targeted graduate topics courses will precede each thematic year, which will then feature research training seminars that develop from the study of fundamental papers to small group research projects. Each year will culminate in an RTG workshop, bringing in external experts and students, and a group retreat for a period of intensive mathematical collaboration. The RTG will also support the highly successful Knots & Graphs REU for OSU undergraduates, involving more faculty and PhD students from algebraic fields, and it will increase the group's participation in other REU activity, particularly the ROMUS (Research Opportunities in Mathematics for Underrepresented Students) program. Further initiatives in improving recruitment and retention for the graduate program include the group's commitment to enhancing the OSU department's work with the Math Alliance (through mentoring and participation in the Field of Dreams Conference) and supporting the department's Directed Reading Program in which graduate students mentor undergraduates on a subject of common interest.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.

代数和几何的相互作用是数学史上的中心故事之一，现代代数几何领域包含了这段历史中积累的许多富有成效的观点。这个研究培训小组在俄亥俄州州立大学将准备在代数几何和相关领域的新一代研究人员，重点是该主题的丰富的观点，从而与其他数学领域的深刻互动。该计划的举措是对社区建设的长期投资：在教师合作中，通过密集的指导关系网络支持学生和博士后的文化，以及加强努力招募和支持代表性不足的群体的成员。由经验丰富的教师领导的五个主题年将包括研究培训研讨会，这将缓解早期博士生向研究的过渡，并将扩大高级博士生和博士后的研究计划;每年年底的会议将加深俄勒冈州立大学集团与外部学者的联系;年度小组务虚会将巩固指导网络，并提供密集的合作机会。该项目还将支持本科生（雷乌斯）的研究经验，包括针对俄亥俄州本科生和来自美国各地代表性不足群体的学生的雷乌斯。这些项目背后加强的教师协调将为多年的研究和培训合作奠定基础，使各级学生和学者受益。15名教师将协调RTG的主要举措，学生和博士后作为导师和学员发挥核心作用。教师将合作运行5个主题年，展示算术，组合和拓扑的角度对代数品种。有针对性的研究生主题课程将在每个主题年之前进行，然后将举办研究培训研讨会，从基础论文的研究到小组研究项目。每年将在RTG研讨会中达到高潮，引入外部专家和学生，并进行一段时间的密集数学合作。RTG还将支持非常成功的结图REU为俄勒冈州立大学本科生，涉及更多的教师和博士生从代数领域，它将增加该集团在其他REU活动的参与，特别是罗马（研究机会数学代表性不足的学生）计划。在提高招聘和保留研究生课程的进一步举措包括该集团的承诺，以加强俄勒冈州立大学部门的工作与数学联盟（通过指导和参加梦想之地会议）并支持该部门的指导阅读计划，在该计划中，研究生指导本科生共同感兴趣的主题。该奖项反映了NSF的法定使命，并被认为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来提供支持。