Abstract: The equivariant quantum cohomology of Grassmannians is an amazing place to study the collision of a number of combinatorial and algebro-geometric phenomena. In this talk, I will introduce an equivariant quantum Pieri rule for Grassmannians (https://arxiv.org/pdf/2010.15395.pdf) that uses the machinery of cylindric shapes in novel ways: it is computationally elegant, requires no recursion, and puts in reach the solutions to a number of additional combinatorial problems. While emphasizing the natural geometric structure of the Grassmannian that this rule illuminates, Iíll also tell the story of this problem, which started with collaboration and conjecture at IAS and continued through periods of both dormancy and deep discussion, as well as the career changes of several of the collaborators. This is joint work with Elizabeth Milićević, Dorian Ehrlich, and Anna Bertiger. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.