John Alford and Ed Swim
Mathematical Modeling of Ecosystems, led by professors John Alford and Edward Swim
Mathematical modeling of ecosystems can provide valuable insight into effective conservation strategies. The focus of this REU project is to create mathematical models related to the coastal wetlands area within the Aransas National Wildlife Refuge (ANWR) and in particular the preservation of a habitat for the migrating whooping cranes, an endangered species, that winter there. We will use data from ANWR and learn to apply relevant mathematical techniques such as numerical simulation, nonlinear differential equations, and linear algebra to analyze and interpret these models.
This project will be informed by results from a previous NSF funded research program (http://www.shsu.edu/~tries_www/ecoimpacs/index.html) that created a multi-model to simulate the ANWR ecosystem. A biology faculty member at SHSU who is actively involved in research within the ANWR ecosystem will lead discussions about the biological foundations of this project.
Students working on this REU project will ultimately help resolve questions of fundamental interest to biologists focused on conserving the ANWR ecosystem by adding components to the multi-model.
Brandy Doleshal and Taylor Martin
Knots and Links, led by professors Brandy Doleshal and Taylor Martin
Knots and links are embedding of circles into three dimensional space. The study of knots and links contributes to many field of mathematics, including topology, geometry, algebra and mathematical biology. In the summer of 2015, we will explore twisted torus knots using algebraic and geometric techniques.
Students will be introduced to link invariants, braids, the symmetric group, graphs and surfaces.
Ken W. Smith
Strongly regular Cayley graphs, led by professor Ken W. Smith
A Cayley graph is a graph which can be defined within a (finite) group. The study of Cayley graphs uses algebraic techniques such as group representations and group homomorphisms. During the summer 2015 SAMREU, we will develop tools from algebraic graph theory, focusing on strongly regular graphs and directed strongly regular graphs which are also Cayley graphs.
During this project, students will be introduced to finite group representations and then will use these tool to resolve open questions in Cayley graphs, focusing on constructing graphs in nonabelian groups.
A first course in Abstract Algebra is necessary for participation in this project.