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We use the Springer correspondence to give a partial characterization of the irre- ducible representations which appear in the Tymoczko dot action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. In type A, we apply these techniques to prove that all irreducible summands which appear in the pushforward of the constant sheaf on the universal Hessenberg family have full support. We also observe that the recent results of Brosnan and Chow, which apply the local invariant cycle theorem to the family of regular Hessenberg varieties in type A, extend to arbitrary Lie type. We use this extension to prove that regular Hessenberg varieties, though not necessarily smooth, always have the “Kahler package.” 

Glioblastoma (GBM) is highly resistant to treatment and invasion into the surrounding brain is a cancer hallmark that leads to recurrence despite surgical resection. With the emergence of precision medicine, patient-derived 3D systems are considered potentially robust GBM preclinical models. In this study, we screened a library of 22 anti-invasive compounds (i.e., NF-kB, GSK-3-B, COX-2, and tubulin inhibitors) using glioblastoma U-251 MG cell spheroids. We evaluated toxicity and invasion inhibition using a 3D Matrigel invasion assay. We next selected three compounds that inhibited invasion and screened them in patient-derived glioblastoma organoids (GBOs). We developed a platform using available macros for FIJI/ImageJ to quantify invasion from the outer margin of organoids. Our data demonstrated that a high-throughput invasion screening can be done using both an established cell line and patient-derived 3D model systems. Tubulin inhibitor compounds had the best efficacy with U-251 MG cells, however, in ex vivo patient organoids the results were highly variable. Our results indicate that the efficacy of compounds is highly related to patient intra and inter-tumor heterogeneity. These results indicate that such models can be used to evaluate personal oncology therapeutic strategies.