research overview
- Dr. Clelland's research uses methods from geometry to study a variety of problems in differential equations, including differential equations that arise naturally in various contexts in differential geometry. Her recent and current research in this area includes the study of dynamic equivalence and dynamic feedback linearization for control systems and isometric immersion of Riemannian manifolds, among other topics. Dr. Clelland also studies the mathematics of redistricting, and in particular, mathematical methods for identifying and quantifying partisan bias in district plans. Since 2021, she has consulted with the Colorado Independent Legislative Redistricting Commission and served as an expert witness for lawsuits challenging proposed redistricting plans in Ohio, Wisconsin, and New York. In her 2022 expert witness report for Nichols v. Hochul, regarding redistricting for the New York State Assembly, she developed new methods for evaluating incumbency protection in redistricting; these methods are the subject of ongoing academic work. In Fall 2023, Dr. Clelland held the position of Research Professor at the Simons-Laufer Mathematical Sciences Institute for a semester-long program on Algorithms, Fairness, and Equity. Also in 2023, she developed a new algorithm to repair gaps and overlaps in a noisy polygonal tiling in a way that preserves the intended adjacency relations as closely as possible. This algorithm has important applications to redistricting, where maps of voting precincts often exhibit such problems that must be repaired prior to analyzing districting plans based on the map. Dr. Clelland has written a Python implementation of this algorithm, which is now included in the MGGG Redistricting Lab's open source Maup package, available at https://github.com/mggg/maup.
