An electric power network is a network of electrical components for generating, transferring, and consuming electric energy. Power networks are of fundamental importance to every aspect of modern life, yet they still lack global stability and are inherently fragile in the sense that sufficiently large disturbances may cause the loss of stability triggering cascading failures. It turns out that understanding how many ways a network can remain stable -- without knowing the exact conditions necessary! -- gives significant insight into how to produce a set of stability conditions.
While motivated from problems in engineering, this project will be purely mathematical in nature. Students will apply techniques from discrete mathematics, geometry, and abstract algebra to help develop a framework for enumerating stability configurations for broad classes of networks. Experience in these areas will be helpful but not necessary; all necessary background in these areas will be provided. There will be an emphasis on using software to produce data, from which conjectures will be made and proven.
Students must have successfully completed MATH 214 and MATH 250 with a B+ or higher. Programming experience is preferred. It is recommended, but not required, that a student have completed a course containing a significant amount of combinatorics, graph theory, and/or abstract algebra.
Number of Student Researchers
Applications open on 01/03/2021 and close on 03/22/2021