John Alford and Ed Swim
Mathematical Modeling of Endangered Ecosystems, led by professors John Alford and Ed Swim
Mathematical modeling of endangered ecosystems can provide valuable insight into effective conservation strategies. Successful environmental modeling requires a hypotheses-based investigation that addresses questions arising due to ecosystem management needs and data collected from that ecosystem.
The ecosystem focus of this REU project is the coastal wetlands area within the Aransas National Wildlife Refuge (ANWR) and in particular the preservation of a habitat for the migrating whooping cranes that winter there. Participants will create mathematical models of the relevant subsystems, analyze their models, and interpret the results in a biologically meaningful way. Effective model creation will be controlled by the relevant biology, and the mathematical tools necessary to analyze the models will depend on the model structure. These tools may include statistical analysis, applications of differential/difference equations, stochastic and deterministic dynamical systems, numerical approximations, agent-based simulations, and optimization methods. 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 that includes both field and laboratory experiments related to ANWR will act as a consultant and lead discussions about the biological foundations of coastal systems. Students working on this REU project will ultimately create and analyze components that can be inserted into the multi-model and help resolve questions of fundamental interest to biologists focused on conserving the ANWR ecosystem.
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 fintie 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.