About the speaker:
Lizzie is a mathematician interested in combinatorial algebraic geometry and geometric structures arising in scattering amplitudes. Lizzie graduated from Berkeley in 2026 under the supervision of Bernd Sturmfels, spent five months as a Chancellor's Fellow at UC Davis, and is now a postdoctoral fellow at Perimeter Institute for Theoretical Physics.
Abstract:
On-shell forms are differential forms on the Grassmannian which represent leading singularities of certain amplitudes. Mathematical investigation of on-shell forms has largely focused on the case of planar graphs, where one can use tools developed by Postnikov in the study of the totally nonnegative Grassmannian. In this talk we develop the mathematics of nonplanar on-shell forms from first principles. In the MHV case (k=2) we give a proof of a determinantal formula appearing in prior physics literature, and exhibit a connection to the hypertree divisors of Castravet and Tevelev. This is based on joint work with Artyom Lisitsyn, Melissa Sherman-Bennett, and Jaroslav Trnka.
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