Algebraic and enumerative combinatorics seminar - Hadleigh Frost-Nested nestings, Moment-Cumulant relations and the Combinatorics of the Cosmos

Abstract: Cosmological correlation functions probe the quantum origins of structure in the universe and are a prototype for many calculations in physics. I will share recent work on the complexes, fans and polytopes associated to these functions based on arXiv:2602.21194 and ongoing work. Two structures lie at the heart of this story: (1) incidence relations between chains and anti-chains, (2) a notion of "nested sets of nested sets". Both structures can be studied for an arbitrary lattice, but building sets of the boolean lattice are my main motivation.