Title: Springer Fibres, Parabolic Induction & Stacking Maps
Abstract: The fibres coming from the Springer resolution on the nilpotent cone are incredibly rich algebraic varieties that have many applications in algebraic geometry, representation theory and combinatorics. In this talk, I will describe how we can use the combinatorics of (bi)tableaux to describe their geometry in low dimensions, and in particular, give a description of their irreducible components. I will also describe a map of Springer fibres resulting from the Lusztig-Spaltenstein construction of parabolic induction from a Levi subalgebra. This is joint work with Lewis Topley, and separately with Mee Seong Im and Arik Wilbert.