Conference on Groups and Computation

群与计算会议

• 批准号: 1719710
• 负责人: Alexei Miasnikov
• 金额: $ 3.78万
• 依托单位: Stevens Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-04-15 至 2018-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1719710&HistoricalAwards=false
• 关键词: Conference; Groups; Computation

This award supports speakers and participants in the conference "Groups and Computation: Interactions between Geometric Group Theory, Computability and Computer Science," to be held at the Stevens Institute of Technology in Hoboken NJ, June 26-30, 2017. The conference will bring together experts in geometric group theory, computability theory and computer science to discuss recent developments and interactions between these subjects, and to create a roadmap for future cooperation. The junior faculty, postdocs, and graduate students attending the conference will benefit from interacting with senior researchers in several disciplines and establishing valuable professional connections and collaborations. In addition to the regular scientific program, the conference will feature a presentation and a discussion on Wikipedia editing in Mathematics, including a practical how-to guide and demonstration.Interaction with computation permeated the development of geometric group theory, from the work of Max Dehn in the 1910s, through the work of Turing in 1930s, the Novikov-Boone Theorem in the 1950s and the theory of word-hyperbolic and automatic groups in the 1990s, to the present day. Now group theorists are interested not just in decidability of various problems but in specific low-complexity estimates. Various data compression techniques (such as straight-line programs, power circuits, etc.) have found amazing applications to group-theoretic decision problems. In turn, geometric group theory has repaid in kind and produced powerful ideas that have found applications in computer science and computability theory. Thus, the notion of "generic-case complexity" as a way of capturing the practical behavior of an algorithm on "most" inputs (and distinct from average-case complexity) was born in geometric group theory. This notion has led to the development of the theory of coarse and generic computability in computational complexity, which is now transforming that subject. The ideas of CAT(0) cubical geometry, coming from geometric group theory, are finding useful applications in computational topology, robotics, and computer science. The conference aims to take stock of these developments and map possible future venues of interaction between geometric group theory, computer science and computability theory. More detailed information can be found at the conference website, http://web.stevens.edu/algebraic/Schupp/

该奖项支持演讲者和与会者在会议“组和计算：几何群论，可计算性和计算机科学之间的相互作用”，将在新泽西州霍博肯的史蒂文斯理工学院举行，2017年6月26日至30日。 会议将汇集几何群论，可计算性理论和计算机科学的专家，讨论这些学科之间的最新发展和相互作用，并为未来的合作制定路线图。 参加会议的初级教师，博士后和研究生将受益于与多个学科的高级研究人员的互动，并建立有价值的专业联系和合作。 除了常规的科学计划外，会议还将介绍和讨论维基百科的数学编辑，包括实用的操作指南和演示。与计算的相互作用贯穿了几何群论的发展，从20世纪10年代的Max Dehn的工作，到20世纪30年代的图灵的工作，从20世纪50年代的Novikov-Boone定理到20世纪90年代的词双曲和自动群理论，一直到今天。现在，群论学家不仅对各种问题的可判定性感兴趣，而且对特定的低复杂性估计感兴趣。各种数据压缩技术（如直线程序、电源电路等）在群论决策问题中发现了惊人的应用。反过来，几何群论也得到了回报，产生了强大的思想，这些思想在计算机科学和可计算性理论中得到了应用。因此，“一般情况复杂度”的概念作为一种捕捉算法在“大多数”输入上的实际行为的方法（与平均情况复杂度不同）诞生于几何群论。这个概念导致了计算复杂性中的粗糙和一般可计算性理论的发展，现在正在改变这个主题。CAT（0）立体几何的思想来自几何群论，在计算拓扑学、机器人学和计算机科学中有着重要的应用。会议旨在评估这些发展，并绘制几何群论，计算机科学和可计算性理论之间相互作用的未来可能场所。更多详细信息可在会议网站http://web.stevens.edu/algebraic/Schupp/上找到