Saiei Matsubara, Twisted Cohomology and Likelihood Ideals

by Saiei Matsubara (Department of Mathematics of Kobe University, Japan)

Tuesday 4 Jul 2023, 11:30 → 12:30 Europe/Rome

P2A (Dipartimento di Fisica e Astronomia - Edificio Paolotti)

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.