GAAG seminar - Periodic pipe dreams for matrix positroid varieties

I will introduce "periodic pipe dreams", a combinatorial model that first appeared in [Fan Guo Su Xiong '25]. I will then give it a full geometric interpretation in terms of new varieties called matrix positroid varieties. Defining these involves infinite matrices that are not simply periodic, as in the case of ordinary positroid varieties, but rather periodically twisted by a diagonal matrix. Matrix positroid varieties are indexed by arbitrary juggling patterns, and we will briefly discuss their combinatorics. We will then calculate their Chern–Schwartz–MacPherson classes using a multiparameter deformation of their characteristic cycles, which we then degenerate into a union of varieties indexed by periodic pipe dreams. This is joint work with Allen Knutson.