8 papers
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…
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…
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…
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 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…
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…