Updated November 19, 2018

## Welcome

James Madison University (JMU) has been chosen for a National Science Foundation Research Experiences for Undergraduates (REU) site in mathematics. All interested undergraduates (who are US citizens or permanent residents) are encouraged to apply for this eight week program, in which students will work in groups of 2-4 under the supervision of their faculty mentors.

## Dates

May 20 2019 - July 12 2019.

## Projects

Automated Identification of Geologic Features: In this project we will use Digital Elevation Models (DEMs) to create mathematical algorithms to identify geologic or geomorphic features such as geologic formations, old landslides and other sites of geohazards that have characteristic surface signatures. The results of the project will be useful for environmental engineers and geologists.

DEMs represent the Earth’s surface at various scales. DEMs can be derived from photogrammetry, radar, and LiDAR (Light Detecting and Ranging) that can be installed on aircraft, vehicles or satellites. The recent boom in drone technology has made photogrammetry and LiDAR more accessible. Currently DEMs are used for generating high resolution topographic dataset that is mostly used for visual identification of land features. We will use our methods to automate this identification.

Students will create mathematical models using techniques from applied mathematics and statistics to solve geological problems. They will also gain experience using R and manipulating real data.

Mentors:

Algebraic and Geometric Invariants of Incidence Structures: Given a relation between two finite sets, it is common to use a matrix to encode the information. Popular examples are the Laplacian matrix of a graph and the point-block incidence matrix of a design. Linear algebraic properties of the matrix can reflect geometric or combinatorial properties of the relation that can otherwise be difficult to detect. For example, the "critical group" of a graph comes from the Laplacian matrix and has order equal to the number of spanning trees of the graph. The critical group of the n-cycle graph is the cyclic group of order n, while the critical group of the n-dimensional cube is unknown. There are many interesting and open problems to be solved!

This project will study and compute such invariants using both discrete and continuous methods, including matrix normal forms, chip firing games, heat flow and similar evolutive models, and numerical experiments.

Mentors:

Housing and a \$4,500 stipend are supplied, as well as full use of university facilities and travel expenses.

## Applications

This REU participates in the Mathematical Sciences REU Common Reply Date agreement. Any student who receives an offer from an REU that participates in the Common Reply Date agreement, including this REU, is not required to accept or decline the offer until March 8, 2019 (or later). The goal of the Common Reply Date agreement is to help students make informed decisions, particularly when faced with the potential of receiving offers from multiple REUs.