4 papers
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…
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…