Twisted Cohomology and Likelihood Ideals

  • Saiei-Jaeyeong Matsubara-Heo
G3 10 (Lecture hall)


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.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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