RTG: Arithmetic, Combinatorics, and Topology of Algebraic Varieties

代数和几何的相互作用是数学历史上的中心故事之一，代数几何的现代领域包含了在这一历史中积累的许多富有成效的观点。俄亥俄州立大学的这个研究培训小组将在代数几何和相关领域培养新一代的研究人员，重点是该学科的丰富视角以及与其他数学领域的深入互动。该项目的举措是对社区建设的长期投资：教员合作，通过密集的师徒关系网络支持学生和博士后的文化，以及加强招募和支持代表性不足群体成员的努力。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，这将有助于早期博士生的研究过渡，并将扩大高级博士生和博士后的研究项目；每年年底的会议将加深俄勒冈州立大学小组与外部学者的联系；一年一度的集体静修将巩固指导网络，并为合作提供密集的机会。该项目还将支持本科生（reu）的研究经验，包括针对俄亥俄州立大学本科生和来自美国代表性不足群体的学生的reu。这些项目背后加强的教师协调将为多年来在研究和培训方面的合作奠定基础，使各级学生和学者受益。15名教师将协调RTG的主要举措，学生和博士后将扮演导师和受指导者的核心角色。教师将合作开展5个主题年，展示代数变种的算术、组合和拓扑观点。有针对性的研究生专题课程将在每个专题年之前进行，然后将以研究培训研讨会为特色，从基础论文的研究发展到小组研究项目。每年都将在RTG研讨会上达到高潮，引入外部专家和学生，并在一段时间内进行密集的数学合作。RTG还将支持俄勒冈州立大学本科生的非常成功的“结&图REU”，涉及更多来自代数领域的教师和博士生，并将增加该小组对REU其他活动的参与，特别是ROMUS（为代表性不足的学生提供数学研究机会）项目。进一步改善研究生项目的招聘和保留的举措包括，该小组承诺加强俄勒冈州立大学与数学联盟的合作（通过指导和参与梦想领域会议），并支持该部门的定向阅读计划，在该计划中，研究生指导本科生共同感兴趣的主题。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

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.