Paving Hessenberg varieties by affines

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Affine pavings of Hessenberg varieties for semisimple groups (2012, background): “Therefore while this theorem generalizes the results of Tymoczko in [10] to a larger collection of nilpotent elements, there are still interesting cases to be considered.”
A positive Monk formula in the S1‐equivariant cohomology of type A Peterson varieties (2009, background): “Hessenberg varieties arise in many areas of mathematics, including geometric representation theory [12, 31, 33], numerical analysis [8], mathematical physics [24, 29], combinatorics [10], and algebraic geometry [5, 6, 34, 35].”
The cohomology rings of regular nilpotent Hessenberg varieties in Lie type A (2015, background): “More generally, geometric properties and invariants of many different types of Hessenberg varieties (including in Lie types other than A) have been widely studied: for instance, the issue of connectedness is addressed in [52, 40], Tymoczko shows that they are not necessarily pure-dimensional in [52]”