133 citations · 554 across the 117 of their papers we have counts for
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Higher convexity for complements of tropical varieties
Mounir Nisse, Frank Sottile
We consider Gromov's homological higher convexity for complements of tropical varieties, establishing it for complements of tropical hypersurfaces and curves, and for nonarchimedea…
Cohomological consequences of the pattern map
Praise Adeyemo, Frank Sottile
Billey and Braden defined maps on flag manifolds that are the geometric counterpart of permutation patterns. A section of their pattern map is an embedding of the flag manifold of…
A primal-dual formulation for certifiable computations in Schubert calculus
Jonathan D. Hauenstein, Nickolas Hein, Frank Sottile
Formulating a Schubert problem as the solutions to a system of equations in either Plücker space or in the local coordinates of a Schubert cell typically involves more equations th…
A combinatorial proof that Schubert vs. Schur coefficients are nonnegative
Sami Assaf, Nantel Bergeron, Frank Sottile
We give a combinatorial proof that the product of a Schubert polynomial by a Schur polynomial is a nonnegative sum of Schubert polynomials. Our proof uses Assaf's theory of dual eq…
Higher convexity of coamoeba complements
Mounir Nisse, Frank Sottile
We show that the complement of the coamoeba of a variety of codimension k+1 is k-convex, in the sense of Gromov and Henriques. This generalizes a result of Nisse for hypersurface c…