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math.AG2025
Avoidance Loci of Real Projective Varieties
Elizabeth Pratt, Kexin Wang
We study real linear spaces in projective space that avoid the real points of a non-degenerate projective variety. For a variety with a real smooth poi…
math.CO2025
Exterior Cyclic Polytopes and Convexity of Amplituhedra
Elia Mazzucchelli, Elizabeth Pratt
The amplituhedron is a semialgebraic set in the Grassmannian. We study convexity and duality of amplituhedra. We introduce a notion of convexity, called \textit{extendable convexit…
math.AG2025
The Segre Determinant
Elizabeth Pratt
The Segre determinant is a polynomial which encodes the condition for points to lie on a bilinear hypersurface in the product of projective spaces. We study Segre determinants and…