## Summer 2019 Projects |

## Mailing addressREU programDept. of Math Sciences Kent State University Math & CS Building Summit Street, Kent OH 44242 ## ContactJenya Soprunovareu [at] math.kent.edu TEL: (330)672-9086 FAX: (330) 672-2209 |
This year we will recruit nine students to work on three projects described below.
We will explore a graph associated with a group. There are many ways to associate a graph to a group. We will look at the graph whose vertices are the nonidentity elements of the group and there is an edge between two elements if they generate a cyclic subgroup. In the paper with Diane Imperatore, we characterized the groups where all of the connected components of this graph are complete graphs. Prerequisites: at least one semester of undergraduate Abstract Algebra.
Change point analysis is a statistical method to identify time points when the system under investigation encounters abrupt changes. High-dimensional time series data are commonly observed in many fields including medical, environmental, financial, engineering and geographical studies. We will study some new methods to detect change points in high-dimensional time series data. The developed methods will span a wide range of topics in applications, including identifying significant genes associated wth certain diseases and cancers and studying dynamic functional connectivity in resting state fMRI data. Prerequisites: some knowledge in Statistical Computing using R or other software; Matrix Theory. Last Summer our REU group, successfully developed some new methods to detect change points in high-dimensional time series data. The developed methods were made to an R package HDcpDetect [Okamoto, J., Stewart, N. and Li, J. (2018). HDcpDetect: detect change points in means of high dimensional data. R Package Version 0.1.0.]. The package is available from https://cran.r-project.org/web/packages/HDcpDetect/. Noncommutative Algebra (Misha Chebotar) This Summer my group will be working on some problems that naturally arise in different areas of Noncommutative Algebra. Possible topics include functional identities; linear preservers; interactions of ring theory, linear algebra and operator theory; radical theory. Prerequisites: Linear Algebra (Theory of Matrices), Abstract Algebra. For the previous projects of my REU groups please visit https://sites.google.com/a/kent.edu/mikhail-chebotar/reu-stude. |