Algebraic and Enumerative Combinatorics Seminar - Lizzie Pratt - On-shell Forms and Hypertree Divisors

Abstract: On-shell forms are differential forms on the Grassmannian which arise in particle physics. They are defined using bipartite graphs with n distinguished boundary vertices. 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, and explain how they arise in physics and math. For certain forms on the Grassmannian Gr(2,n), we prove a determinantal formula appearing in the physics literature, and give a connection to the hypertree divisors of Castravet and Tevelev.

This is joint work with Artyom Lisitsyn, Melissa Sherman-Bennett, and Jaroslav Trnka.

There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.