One area of my research concerns developing theorems which can be used to rigorously detect that a political districting is gerrymandered—that is, drawn to optimize some partisan goal. In particular, the papers Assessing significance in a Markov chain without mixing and Separating effect from significance in Markov chain tests (with Chikina and Frieze for the first, and with Chikina, Frieze and Mattingly for the second) both develop theorems explicitly with this goal.
I gave a high-level overview of the ideas behind these methods in a TedX talk at CMU in 2018:
Wired magazine also has a nice article about the League of Women Voters v. Commonwealth of Pennsylvania lawsuit that discusses my testimony in that case.
Based on the techniques developed in our papers, I've testified as an expert witness in three lawsuits which went to trial.
My testimony in this case was based on the technique developed in our first paper (Assessing significance in a Markov chain without mixing). This case concerned the U.S. Congressional districting of Pennsylvania. The PA Supreme Court found the districting to be an unconstitutional partisan gerrymander, and it was redrawn. The new map was first used in the 2018 midterm elections.
My testimony in this case was based on the technique developed in our second paper (Practical tests for significance in Markov chains). This case concerned the state-level House and Senate districtings of North Carolina. North Carolina has an interesting constraint on districtings which requires them to respect a county clustering of the state; using the new method allowed both richer qualitative statements to be made about the evaluated districtings, and allowed uniform levels of statistical significance to be employed even across county clusters where the degree of outlier-status varied. The court found the map to be an unconstitutional partisan gerrymander and the legislature declined to appeal. A new map was used in 2020.
My testimony in this case was again based on the technique developed in our second paper (Practical tests for significance in Markov chains). This case concerned the Congressional districting and the state-level House and Senate districtings of North Carolina. The NC supreme court initially ordered new maps drawn for all three districtings, but then reversed itself after a change in the make-up of the court.