REU site: Complexity Across Disciplines (CAD)

This grant funds the REU site 'Complexity Across Disciplines' at Boise State University, hosted in the Department of Mathematics. This site seeks to produce cohorts of young researchers whose work and vision transcend current boundaries between STEM disciplines. The research mentors will each engage a team of nationally recruited undergraduate students in a research project with strong interdisciplinary scope and based on finitary mathematical structures. The mathematical foundations for these projects include algebraic structures, combinatorial structures and game theory. Each of the cohorts of ten REU researchers will be thoroughly engaged in contemporary research problems with applications to cryptology, biology and several other fields of inquiry. The projects have deep connections with important open problems in mathematics, and could lead to discoveries of importance to the security of currently commercially used cryptosystems. The idea to examine certain genomic rearrangement processes from a game-theoretic point of view is new to the field, has inherent value as a mathematical exploration, and has the potential to clarify observed phenomena in natural rearrangement processes. The study of splitting systems could give new insights into mathematical tools for medical, chemical and electrical testing as well as error correction.

The nature of computing and complexity has expanded from the academic to the practical arena through great strides in scientific understanding of basic processes of life, the biggest transformation in information processing in history through invention of the internet, and automation of all basic tasks in our daily lives. The need to understand fundamental limitations on computing, thus on basic processes of life, daily living and information processing, has never been greater. The research projects featured at this site ultimately relate to the question of limitations on computing. The motivations for the offered projects arise from the quest for efficient search or sorting algorithms and for efficient information security tools. The research direction of this REU program and its projects are guided by experienced mentors that include an early career investigator, a female researcher and a senior scientist. Through its recruitment process this program brings undergraduate research experiences to students from institutions across the nation where such opportunities are limited. By involving the REU students in intellectual outreach activities targeting K-12 students through the REU site's partnership with the NASA funded Idaho Science and Aerospace Scholars, students from rural communities with limited opportunities have one-on-one exposure to highly motivated STEM students from across the nation. This outreach activity has the potential to transform the vision of the K-12 students about their own careers in a STEM field. The site offers, in collaboration with several other summer undergraduate research programs at Boise State University, a rich array of professional and interdisciplinary development events.