William Martin, professor of mathematical sciences, has received a three-year, $150,000 grant from the National Science Foundation for a research project titled, “Association Schemes and Configurations in Real and Complex Space.”
The project is aimed at taking on questions that have stumped the best mathematical minds in the world for decades. Martin is looking to advance mathematicians’ understanding of association schemes, which are finite combinatorial structures that can be viewed algebraically, geometrically, or as highly symmetric networks.
Finding new association schemes, or even better understanding them, could enable researchers to use one quantum computer to simulate another. They also could be used to discover new error-correcting codes for digital communications, new spherical designs for estimating solutions to calculus problems in high-dimensional space, or new secure scrambling components for symmetric key encryption.
Martin is working on underlying algebraic theorems that will lead to a stronger mathematical theory, though he said he is focused on making advances that other researchers can then use in their own work, to solve problems in various applied areas.
At least one PhD student and multiple MQP teams will be working on the project.
Award Date: Aug. 2, 2018