Abstract: 

I will discuss how Young tableaux arise from the Plucker map. Influential work of Hodge from the 1940s led the way in using Grobner bases to combinatorially study the Grassmannian. In the past decade, the work of Knutson-Lam-Speyer has brought to the fore the significance of positroid subvarieties in the Grassmannian. I will explain how to use Young tableaux to understand these subvarieties and thereby how to connect promotion on Young tableaux with the cyclic symmetry of positroid varieties. This is based on joint work with Ayah Almousa and Daoji Huang, see arxiv.org/abs/2309.15384.