Speaker: Elizabeth Drellich, Swarthmore
Abstract: The Hessenberg varieties are an expansive family of subvarieties of the flag variety determined by two parameters: an element 
of the Lie algebra 
and a subspace 
. These two parameters let us encode all sorts of combinatorial data into Hessenberg varieties in order to use geometric methods on combinatorial problems. But while they are powerful tools, even basic questions about Hessenberg varieties, such as when two Hessenberg varieties are equal, can be hard to answer.
This talk will present the containment poset on Hessenberg varieties with a fixed parameter . We will discuss recent results about the poset's structural relationship to Young's lattice and show that a natural involution of the poset extends to a homeomorphism of algebraic varieties.