Workshop on Arithmetic and Topology Over Global Fields

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The award will fund participation in a workshop titled "Arithmetic and topology over global fields," to be held October 7-9, 2022 at the University of Wisconsin-Madison. This workshop will focus on developments at the interface between two different fields of math, number theory and topology. The workshop will bring together early-career mathematicians from both subjects in order to spur further progress at this already-active boundary between fields. Funding will be concentrated on graduate students, postdocs, and researchers without other federal funding. Our conference also focuses on inclusiveness in the math community by inviting many high-profile early-career female mathematicians, and will apply to set up the conference in cooperation with the Association for Women in Mathematics. A webpage with up-to-date information about the workshop can be found at this link: https://sites.google.com/view/october-workshop/home. Questions pertaining to monodromy have been highly influential on recent work in areas like rational and integral points on varieties, special points, unlikely intersections, statistics of Selmer groups, etc. Many fundamental conjectures about motives or algebraic cycles are also deeply connected to monodromy. This conference aims to bring together experts on various topological aspects of varieties defined over arithmetic bases to give talks to a wider audience consisting of graduate students, postdoctoral researchers and other mathematicians working in arithmetic geometry. We also aim for the workshop to be an environment for the participants at all levels to meet and talk in person, and seek new collaborations, creating impact throughout the field. We hope that the diversity of topics and talks given by senior participants in the workshop will provide a fantastic opportunity for the junior participants to learn about new developments and questions in the field. We provide a 2-hour poster session for the junior participants, especially graduate students, to present their projects and results to experts and peers. Our advertisement and recruitment will prioritize graduate students and early-career researchers, who stand to benefit the most from an introduction to this quickly-moving area.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.