Upon the release of new Census data in 2021, the contentious, decennial redistricting cycle was kicked off. Census data informed the drawing of new maps, but battles over which maps to enact are still being fought in courts. Presently, mathematical analyses are the crux of redistricting litigation. Within this talk, I’ll describe some of the mathematical elements of redistricting: from quantifying partisan fairness of a district to creating millions of maps to provide a basis for what’s typical. In particular, I’ll focus on racially polarized voting analysis; a technique used in voting rights lawsuits to determine whether different racial groups have distinct voting preferences. I’ll also give some insight into the algorithmic creation and graph theoretic considerations that go into the creation of millions of maps.

What do you think about when you think about gerrymandering? Probably you think about a lack of proportionality: ``party A won 54% of the votes but only 37% of the districts!'' Or maybe you think about funny-shaped districts that look like they were drawn by a cartoon artist (google ``Goofy kicking Donald Duck'' if you'd like to see an example). Unfortunately, these commonly-held beliefs about the signs of gerrymandering are not particularly well-founded. And doubly unfortunately, while these are not accurate ways to detect gerrymandering, a lot of the other recently-proposed metrics intended to detect gerrymandering are *also* not very accurate! Luckily, whenever we encounter a hard problem, mathematicians dive in to find solutions. In this talk, I'll discuss why looking at shapes and focusing on proportionality is not an accurate way to find gerrymandering, and I'll also discuss why metrics like the Efficiency Gap and others don't work well. We'll then discuss why outlier analysis (the gold standard) and the GEO metric (a much easier to compute deterministic metric) are proving to be much more useful in this arena.