Resonance Varieties of Schubert Matroids

Prajwal Dhondiram Udanshive (Western University)

Resonance varieties of Orlik-Solomon algebras are cohomologically-defined matroid invariants motivated by geometry. While the resonance in cohomological degree 1 has been extensively studied, understanding the resonance in higher degrees is elusive. In this talk, we see that the cohomology of Schubert matroids admits a decomposition based on the cyclic flats, giving a complete characterization of the jump loci using lattice path combinatorics. Generalizing a result of Hattori, we see that the complex Schubert arrangement complement is a toric complex up to a homotopy equivalence. The talk is based on a joint work with Graham Denham.

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