Arithmetic, Algebra, and Algorithms

该奖项为美国的参与者提供资金，特别强调早期职业研究人员和代表性不足的群体成员，参加2020年4月13日至17日在英国爱丁堡国际数学科学中心（ICMS）举行的“算术，代数和算法”研讨会（https：//www.icms.org.uk/AAA.php）。 研讨会的主要目标是汇集算法，数论，代数和密码学领域的研究人员。这次会议将成为这些社区之间交流的催化剂，并为早期职业研究人员提供快速进入这些快速发展领域的机会。 除了理论数学的众多应用外，这些领域通过真实的世界与计算机安全的联系具有巨大的重要性。 这些领域的重大成就对现代生活的许多方面产生了直接而深远的影响。算术统计学研究家庭中数论对象的行为。 该领域中一些最著名的问题可以追溯到高斯，但在过去的15年里，该领域一直在经历着爆炸式的活动和惊人的成功，在不久的将来有着巨大的发展潜力。 数学数论和代数涉及数论和代数结构中的快速计算，并在密码学中有重要的应用。 密码学中的新思想、新构造和新问题给数学家带来了许多有趣的问题。 从历史上看，密码学、数论、算法和代数的发展相互影响，社区依赖于富有成效的互动。 讲习班将把这些社区聚集在一起，在他们之间建立进一步的互动，并将有助于人力资源的发展，在数学科学的早期职业研究人员接触到最多的，该奖项反映了NSF的法定使命，并被认为值得支持通过使用基金会的知识价值和更广泛的影响审查标准进行评估。

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.