9 citations · 9 across the 9 of their papers we have counts for
9 papers
Conormal Rank of Subvarieties of Grassmannians
Elizabeth Pratt
The cotangent space to any subvariety of a Grassmannian is naturally identified with a space of linear homomorphisms. We use this to define a new statistic on a subvariety of a Gra…
Multigraded Hurwitz forms
Elizabeth Pratt, Luca Sodomaco, Bernd Sturmfels
The Hurwitz form of a projective variety characterizes linear spaces of complementary dimension which meet the variety non-transversally. We extend this notion to varieties in a pr…
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…
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…
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…
Chow-Lam Recovery
Elizabeth Pratt, Kristian Ranestad
We study the conditions under which a subvariety of the Grassmannian may be recovered from certain of its linear projections. In the special case that our Grassmannian is projectiv…
FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
Elliot Glazer, Ege Erdil, Tamay Besiroglu +21
We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most…
Wondertopes
Sarah Brauner, Christopher Eur, Elizabeth Pratt +1
Positive geometries were introduced by Arkani-Hamed--Bai--Lam as a method of computing scattering amplitudes in theoretical physics. We show that a positive geometry from a polytop…
The Chow-Lam Form
Elizabeth Pratt, Bernd Sturmfels
The classical Chow form encodes any projective variety by one equation. We here introduce the Chow-Lam form for subvarieties of a Grassmannian. By evaluating the Chow-Lam form at t…