Séminaire Calcul Formel

Twisted Cohomology and Likelihood Ideals

by Saiei Matsubara

XR203 (XLIM)




In this talk, we study a hypergeometric integral associated 
with any Laurent polynomial. It is called Feynman integral in physics 
and called marginal likelihood integral in statistics. A twisted 
cohomology group is a system of difference equations that hypergeometric 
integral satisfies. This is a left ideal in a non-commutative ring. It 
naturally "converges to" likelihood equations previously studied in 
algebraic statistics. The converse operation exists in principle: the 
likelihood equation knows the twisted cohomology. We will clarify the 
meaning of this statement. Based on joint work with Simon Telen (MPI 
MiS) arXiv:2301.13579.