Séminaire Calcul Formel

Computing cohomology intersection numbers of GKZ systems

by Dr Saiei-Jaeyeong MATSUBARA-HEO (Kobe University)




In the theory of special functions, a particular kind of
multidimensional integral appears frequently. It is called the Euler
integral. In order to understand the topological nature of the integral,
twisted de Rham cohomology theory plays an important role. In this talk,
we propose an algorithm of computing an invariant "cohomology intersection
number". The algorithm is based on the fact that the Euler integral
satisfies a GKZ system and utilizes algorithms to find rational solutions
of differential equations. This talk is based on a joint work with Nobuki
Takayama. The main article is available here: http://www.math.kobe-u.ac.jp/OpenXM/Math/intersection2/Article4.pdf