Speaker: Bü?ra Atar (McMaster University)
Title: Hessenberg Patch Ideals
Abstract: Hessenberg varieties are subvarieties of the full flag variety. After defining the Hessenberg patch ideal of a regular nilpotent Hessenberg variety, we will talk about some problems asked about Hessenberg patch ideals for indecomposable Hessenberg functions.
Speaker: Adrian Cook (McMaster University)
Title: Lattice Groupoids: An Introduction
Abstract: A lattice groupoid is a collection of lattices equipped with piecewise linear maps between them. Similar to algebraic tori, which can be associated to their dual lattices of characters and cocharacters, we can associate a more general class of algebras to dual lattice groupoids. We will discuss how lattice groupoids can be constructed from cluster algebras and give examples to illustrate important concepts related to the theory of lattice groupoids. Finally, we will discuss results and future directions for inquiry in this area.