REU site: Complexity Across Disciplines

这笔赠款为博伊西州立大学的本科生研究体验(REU)网站“跨学科复杂性”提供了资金，这是一个为期9周的项目，每年夏天有8名学生参加。该项目由数学系主办，重点关注与计算复杂性相关的项目。该网站寻求培养一批年轻的研究人员，他们的工作和视野超越了STEM学科的传统界限。每个队列将从事当代数学研究问题，应用于密码学、生物学和其他几个研究领域。该计划还将为REU学生提供机会，参加针对该地区K-12学生的外联活动。来自机会有限的农村社区的学生将有机会一对一地接触到来自全国各地积极进取的STEM学生。该网站与博伊西州立大学的其他暑期本科生研究项目合作，提供了一系列丰富的专业和跨学科发展活动。计算和复杂性的性质已经从学术领域扩展到实践领域，因为在对生命基本过程的科学理解方面取得了长足的进步，通过互联网的发展在信息处理方面取得了重大进展，以及基本日常任务的自动化。这些研究项目的动机是寻求高效的搜索或排序算法和高效的信息安全工具。这些项目的数学基础包括代数结构、组合结构和博弈论。每个项目都与数学中的重大公开问题有深刻的联系，并可能导致对当前商业使用的密码系统的安全性和数据挖掘具有重要意义的发现。从博弈论的角度检查某些基因组重排过程的想法是新的，作为一种数学探索具有内在的价值，并有可能澄清在自然重排过程中观察到的现象。

This grant funds the Research Experience for Undergraduates (REU) site "Complexity across Disciplines" at Boise State University, a nine-week program for eight students each summer. The program, hosted in the Department of Mathematics, focuses on projects related to computational complexity. The site seeks to produce cohorts of young researchers whose work and vision transcend traditional boundaries among STEM disciplines. Each cohort will engage in contemporary research problems in mathematics, with applications to cryptology, biology, and several other fields of inquiry. The program will also provide opportunities for REU students to participate in outreach activities targeting K-12 students in the region. Students from rural communities with limited opportunities will have one-on-one exposure to highly motivated STEM students from across the nation. The site offers, in collaboration with other summer undergraduate research programs at Boise State University, a rich array of professional and interdisciplinary development events.The nature of computing and complexity has expanded from the academic realm to the practical arena through great strides made in the scientific understanding of basic processes of life, significant advances in information processing through the growth of the internet, and automation of basic daily tasks. The research projects are motivated by a quest for efficient search or sorting algorithms and for efficient information security tools. The mathematical foundations for these projects include algebraic structures, combinatorial structures, and game theory. Each project has deep connections with significant open problems in mathematics, and could lead to discoveries of importance to the security of current commercially used cryptosystems and to data mining. The idea of examining certain genomic rearrangement processes from a game-theoretic point of view is new, has inherent value as a mathematical exploration, and has the potential to clarify observed phenomena in natural rearrangement processes.