# Stratifications of the spaces of momenta and masses in perturbative quantum field theories

SEMINARS: HARVARD-MIT COMBINATORICS

**When:**October 30, 2024

**Where:**MIT, Room 2-132

**Speaker:**Stan Srednyak (Duke University)

In perturbative quantum field theory, the analytic structure of amplitudes is tightly related to the properties of a family of stratifications on the space of kinematic invariants and masses. There are two types of stratifications. In one of them, strata are defined by fixing the topological type of the intersection of Feynman quadrics. In the other, the stratification is defined by fixing the intersection type of Landau varieties. For each Feynman diagram, the strata are enumerated by subdiagrams of the original diagram. For a given quantum field theory, there is an infinitely generated algebra that enumerates these spaces. We relate these spaces to exactness properties of certain multigraded complexes associated with the Feynman graph. There are multiple connections to the theory of generalized hypergeometric functions and higher discriminants (in the sense of Gelfand Kapranov and Zelevinsky) and toric geometry. In this talk, after a thorough introduction, I will focus on geometric and combinatorial aspects of these stratifications.

For information about the Richard P. Stanley Seminar in Combinatorics, visit https://math.mit.edu/combin/