RTG: Arithmetic, Combinatorics, and Topology of Algebraic Varieties

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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.