Arithmetic of Function Fields and Diophantine Geometry
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This award supports mathematicians from US institutions to participate at the conference Arithmetic of Function Fields and Diophantine Geometry, to be held on May 20-24, 2019, at the National Center for Theoretical Sciences (NCTS) on the campus of National Taiwan University in Taipei, Taiwan. The purpose of the conference will be to bring together both established and junior researchers in Number Theory from across the globe, and especially researchers in Function Field Arithmetic, Diophantine Geometry, and related fields. Primary goals will be to discuss recent advances in these areas and to encourage further research and future collaboration, and one important aspect of the conference will be to increase participation of junior researchers. In addition to twenty invited speakers ranging from established mathematicians to recent Ph.D.''s, the schedule will include 6-8 contributed talks by graduate students and post-doctoral researchers. The conference website is http://www.ncts.ntu.edu.tw/events_2_detail.php?nid=216.Since early work of Artin and Weil in the last century, it has been known that the study of function fields of algebraic curves over finite fields in positive characteristic runs in close analogy with the study of number fields. At the same time Diophantine geometry also applies techniques from algebraic geometry to problems in number theory, and so the two subjects are closely intertwined in their efforts to resolve deep problems in number theory using geometric methods. The conference will focus on aspects of function field arithmetic and Diophantine geometry that strengthen common points of view and present opportunities for cross-pollination of ideas, including modular forms and Galois representations, special values of L-functions, arithmetic dynamics, and rational points on varieties. These topics are on the forefront of research in Number Theory, and there have been several major advances in these areas in recent years. The conference will afford participants the opportunities to communicate their research with a broader mathematical community and to initiate new research projects that advance these important areas of Number Theory.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.