RTG: Arithmetic, combinatorics, and topology of algebraic varieties at The Ohio State University is a $2.1M research and training grant sponsored by the National Science Foundation as DMS-2231565.

Funds are used to support activities for undergraduates, graduate students and postdoctoral scholars. Several of these will be done in collaboration with those of the Math Alliance and the local student chapters of the AWM (the Association for Women in Mathematics), SACNAS (Society for Advancement of Chicano/Hispanics and Native Americans in Science) and the OSU LGBTQ+ in Math Alliance.

Publications and preprints of our group related to this project are available at the arXiv.org preprint server and listed here.

The YouTube channel of the RTG group has a record of the talks delivered at each of the RTG conferences and similar events taking place at OSU during the grant period.

Fellowship funds from this grant can only be used to support U.S. citizens, nationals, and permanent residents.

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 five 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.

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