A key aspect of this research is the geometric notion of the compactness of a given political district, a numerical measure that attempts to quantify how extensively gerrymandered it is.
[12] “What courts have been looking for is one definition of compactness that they can understand, that we can compute, and that they can use as a kind of go-to standard”, she said in an interview with The Chronicle of Higher Education.
[13] To help tackle the challenge of finding an agreed-upon standard, Duchin has developed a long-term, wide-ranging project on the mathematics of gerrymandering.
[13] As a part of this project, she founded a summer program to train mathematicians to become expert witnesses in related legal cases.
[17] In 2018, Governor of Pennsylvania Tom Wolf enlisted Duchin to help him evaluate newly drawn redistricting maps for fairness.
[18] This happened as a consequence of the Supreme Court of Pennsylvania decision which declared the state's 2011 US congressional districting map to be unconstitutional.
In 2022, a panel of judges threw out Alabama's soon-to-be-used congressional maps, citing the fact that the percentage of black people in the state had risen to about a quarter of the population.