Arithmetic, Algebra, and Algorithms

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This award funds US-based participants, with special emphasis on early-career researchers and members of underrepresented groups, to attend the workshop "Arithmetic, Algebra, and Algorithms"(https://www.icms.org.uk/AAA.php), April 13-17, 2020, at the International Centre for Mathematical Sciences (ICMS) in Edinburgh, UK. The main goal of the workshop is to bring together researchers in the areas of algorithms, number theory, algebra, and cryptography. This meeting will serve as a catalyst for exchange among these communities, as well as offering early-career researchers a rapid entry into these fast developing fields. In addition to numerous applications to theoretical mathematics, these fields have immense importance through real world connections to computer security. Major successes in these areas have immediate and profound effects on many facets of modern life.Arithmetic statistics studies the behavior of number theoretic objects in families. Some of the most famous problems in the field go back to Gauss, but in the last 15 years the field has been experiencing an explosion of activity and spectacular success, with great potential for further developments in the near future. Algorithmic number theory and algebra are concerned with fast computation in number theoretic and algebraic structures, and have important applications to cryptography. New ideas, constructions, and questions in cryptography lead to interesting problems for mathematicians. Historically, developments in cryptography, number theory, algorithms, and algebra have influenced each other, and the communities depend on fruitful interaction. The workshop will bring together these communities, building further interactions among them, and will contribute to the development of human resources in the mathematical sciences by exposing early-career researchers to the most up-to-date advances in these fields and by allowing them the opportunity to interact with senior mathematicians drawn from the top researchers worldwide.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.