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Séminaire Calcul Formel
# Twisted Cohomology and Likelihood Ideals

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XR203 (XLIM)
### XR203

#### XLIM

Description

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.