Conference on Groups and Computation

该奖项支持发言人和与会者在会议“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，”将在霍博肯新泽西，6月26日至30日举行的史蒂文斯理工学院。会议将汇集几何群论、可计算理论和计算机科学方面的专家，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，并建立宝贵的专业联系和合作。除了常规的科学项目外，会议还将有一个关于维基百科在数学中的编辑的演讲和讨论，包括一个实用的指导和演示。从20世纪10年代马克斯·德恩的工作，到20世纪30年代图灵的工作，从20世纪50年代的诺维科夫-布恩定理到20世纪90年代的词双曲和自动群理论，再到今天，与计算的相互作用渗透到几何群论的发展中。现在群理论家不仅对各种问题的可决性感兴趣，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、功率电路等）在群论决策问题中得到了惊人的应用。反过来，几何群论也得到了回报，并产生了强大的思想，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，作为捕获算法在“大多数”输入（不同于平均情况复杂性）上的实际行为的一种方式，“一般情况复杂性”的概念诞生于几何群论。这个概念导致了计算复杂性中粗糙和一般可计算性理论的发展，现在正在改变这一主题。CAT(0)立方几何的思想来自几何群论，在计算拓扑、机器人和计算机科学中得到了有用的应用。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理论之间可能的未来互动场所。更详细的信息可以在会议网站http://web.stevens.edu/algebraic/Schupp/上找到

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/