Lizzie Pratt

PhD student

I am broadly interested in combinatorial algebraic geometry.

Papers:

Chow-Lam Recovery (preprint, with Kristian Ranestad)
We explore the extend to which a subvariety of the Grassmannian can be uniquely recovered from its Chow-Lam form. Unlike the classical case of Chow forms for projective varieties, this is not always possible, and we provide several interesting families of counter-examples.
.
Wondertopes (preprint, with Sarah Brauner, Chris Eur, and Raluca Vlad)
We provide a new type of positive geometry called a wondertope (wonderful polytope). It is constructed by pulling back an open region of a hyperplane arrangement to the wonderful compatification of the arrangement, then taking the Euclidean closure.
The Chow-Lam Form (preprint, with Bernd Sturmfels)
We introduce the Chow-Lam form for subvarieties of the Grassmannian, generalizing the classical Chow form. This gives us universal formulas for projections between Grassmannians and their branch loci.
Combinatorics of m=1 Grasstopes (preprint, with Yelena Mandelshtam and Dmitrii Pavlov)
Grasstopes are a generalization of amplituhedra. Building on work of Karp and Williams on the m=1 amplituhedron, we show that m=1 Grasstopes consist of regions of a hyperplane arrangement characterized by a sign condition.
D-Module Techniques for Solving Differential Equations in the Context of Feynman Integrals (Letters in Mathematical Physics 2024, with Johannes Henn, Anna-Laura Sattelberger, and Simone Zoia)
We use D-module methods to construct series solutions to linear differential equations appearing in the context of Feynman integrals.
On the Geometry of Elliptic Pairs ( Journal of Pure and Applied Algebra 2023)
In this paper we classify toric elliptic pairs of Picard number two. These elliptic pairs are used to construct examples of surfaces whose pseudo-effective cone is non-polyhedral for a set of primes of positive density, and, assuming the generalized Riemann hypothesis, polyhedral for a set of primes of positive density.
Quantum Jacobi forms and sums of tails identities (Research in Number Theory 2022, with Amanda Folsom, Noah Solomon, and Andrew Tawfeek)
We discover new examples of hypergeometric series which are quantum Jacobi forms, i.e. satisfy a modular transformation property up to an analytic error term.