Jeffrey Giansiracusa: A moduli perspective on Grassmannians and matroids in idempotent algebra

Abstract: Grassmannians are an important example of moduli spaces in algebraic geometry (over rings). In this talk I will explore and contrast several distinct notions of Grassmannians that appear when passing to the setting of idempotent semirings. There is: (1) a moduli space of locally free quotients, which has an interesting topology but might not be representable; (2) the Dressian, which is described elegantly in terms of an idempotent version of exterior algebra; and (3) various tropicalizations of Grassmannians. I will discuss these objects from a scheme-theoretic and moduli-theoretic point of view.v