instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Integral representations of GKZ hypergeometric systems
Seminario de Álgebra
 Fecha: 18.09.2018 11.00 Lugar: Seminario I (IMUS), Edificio Celestino Mutis Autor: Matsubara-Heo Saiei-Jaeyeong
GKZ (Gelfand, Kapranov, Zelevinsky) system is a certain holonomic system on an Affine space whose basis of solutions can be constructed in terms of hypergeometric series ($\Gamma$-series). We show that GKZ hypergeometric system has various realisations as twisted Gauss -Manin connections: Laplace type, Euler-Laplace type, and Residue-Laplace type. In particular, when GKZ system is regular holonomic, this realisation combined with Riemann-Hilbert correspondence yields a new description of its solution sheaf on non-singular locus. If time permits, we will discuss its relation to intersection theory of twisted cycles and some other related works.

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