Intersecting two matroids is a central problem in combinatorial optimization. However, intersecting three matroids is already NP-hard. In this talk, I will present the best-known algorithms to compute the intersection of more than two (representable) matroids, based on an algebraic framework around partial differential operators, with tight connections to competing determinant-based sieving methods (Eiben-Koana-Wahlström, arxiv '23).
The material of this talk is based on joint work with Kevin Pratt, Viktoriia Korchemna and Michael Skotnica.