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  1. (, Contemporary Mathematics, American Mathematical Society)
    Tu, Loring W (Ed.)
    We aim in this manuscript to describe a specific notion of geomet- ric positivity that manifests in cohomology rings associated to the flag variety G/B and, in some cases, to subvarieties of G/B. We offer an exposition on the the well-known geometric basis of the homology of G/B provided by Schubert varieties, whose dual basis in cohomology has nonnegative structure constants. In recent work [R. Goldin, L. Mihalcea, and R. Singh, Positivity of Peterson Schubert Calculus, arXiv2106.10372] we showed that the equivariant cohomology of Peterson varieties satisfies a positivity phenomenon similar to that for Schubert calculus for G/B. Here we explain how this positivity extends to this particular nilpotent Hessenberg variety, and offer some open questions about the ingredients for extending positivity results to other Hessenberg varieties. 
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