53 citations · 94 across the 18 of their papers we have counts for
21 papers
Principal Matroid Determinants
Saiei-Jaeyeong Matsubara-Heo, Simon Telen
We develop a theory of principal determinants and hypergeometric systems for realizable matroids. Our framework parallels the toric theory of Gel'fand, Kapranov, and Zelevinsky (GK…
Periods of Limiting Mixed Hodge Structures of Projective Hypersurfaces
Masanori Asakura, Saiei-Jaeyeong Matsubara-Heo
For a generic one-parameter degeneration of projective hypersurfaces, we show that the periods of the limiting mixed Hodge structure are generated by certain special values of loga…
Differential Space of Feynman Integrals: Annihilators and -module
Vsevolod Chestnov, Wojciech Flieger, Pierpaolo Mastrolia +3
We present a novel algorithm for constructing differential operators with respect to external variables that annihilate Feynman-like integrals and give rise to the associated $\mat…
Hypergeometric Discriminants
Saiei-Jaeyeong Matsubara-Heo
Given a family of varieties, the Euler discriminant locus distinguishes points where Euler characteristic differs from its generic value. We introduce a hypergeometric system assoc…
Euler Discriminant of Complements of Hyperplanes
Claudia Fevola, Saiei-Jaeyeong Matsubara-Heo
The Euler discriminant of a family of very affine varieties is defined as the locus where the Euler characteristic drops. In this work, we study the Euler discriminant of families…
Generalized hypergeometric functions with several variables
Saiei-Jaeyeong Matsubara-Heo, Toshio Oshima
We introduce a hypergoemetirc series with two complex variables, which generalizes Appell's, Lauricella's and Kempé de Fériet's hypergeometric series, and study the system of diffe…
Four Lectures on Euler Integrals
Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera, Simon Telen
These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals…
Restrictions of Pfaffian Systems for Feynman Integrals
Vsevolod Chestnov, Saiei J. Matsubara-Heo, Henrik J. Munch +1
This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering ampl…
Twisted cohomology and likelihood ideals
Saiei-Jaeyeong Matsubara-Heo, Simon Telen
A likelihood function on a smooth very affine variety gives rise to a twisted de Rham complex. We show how its top cohomology vector space degenerates to the coordinate ring of the…
Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
Vsevolod Chestnov, Federico Gasparotto, Manoj K. Mandal +4
We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose…
Localization formulas of cohomology intersection numbers
Saiei-Jaeyeong Matsubara-Heo
We revisit the localization formulas of cohomology intersection numbers associated to a logarithmic connection. The main contribution of this paper is threefold: we prove the local…
A tree expansion formula of a homology intersection numbers on the configuration space
Saiei-Jaeyeong Matsubara-Heo
In \cite{M}, Sebastian Mizera discovered a tree expansion formula of a homology intersection number on the configuration space . The formula originates in a stud…
Global analysis of GG systems
Saiei-Jaeyeong Matsubara-Heo
This paper deals with some analytic aspects of GG system introduced by I.M.Gelfand and M.I.Graev: we compute the dimension of the solution space of GG system over the field of func…
Computing cohomology intersection numbers of GKZ hypergeometric systems
Saiei-Jaeyeong Matsubara-Heo
In this review article, we report on some recent advances on the computational aspects of cohomology intersection numbers of GKZ systems developed in \cite{GM}, \cite{MH}, \cite{MT…
Homology and cohomology intersection numbers of GKZ systems
Yoshiaki Goto, Saiei-Jaeyeong Matsubara-Heo
We describe the homology intersection form associated to regular holonomic GKZ systems in terms of the combinatorics of regular triangulations. Combining this result with the twist…
An algorithm of computing cohomology intersection number of hypergeometric integrals
Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama
We show that the cohomology intersection number of a twisted Gauss-Manin connection with regularization condition is a rational function. As an application, we obtain a new quadrat…
Euler and Laplace integral representations of GKZ hypergeometric functions
Saiei-Jaeyeong Matsubara-Heo
We introduce an interpolation between Euler integral and Laplace integral: Euler-Laplace integral. We establish a combinatorial method of constructing a basis of the rapid decay ho…
On Mellin-Barnes integral representations for GKZ hypergeometric functions
Saiei-Jaeyeong Matsubara-Heo
We consider Mellin-Barnes integral representations of GKZ hypergeometric equations. We construct integration contours in an explicit way and show that suitable analytic continuatio…
Laplace, Residue, and Euler integral representations of GKZ hypergeometric functions
Saiei-Jaeyeong Matsubara-Heo
We consider four types of representations of solutions of GKZ system: series representations, Laplace integral representations, Euler integral representations, and Residue integral…
On the rapid decay homology of F.Pham
Saiei-Jaeyeong Matsubara-Heo
In \cite{hien}, M. Hien introduced rapid decay homology group $\Homo^{rd}_{*}(U, (\nabla, E))$ associated to an irregular connection on a smooth complex affine variet…
Residue current approach to Ehrenpreis-Malgrange type theorem for linear differential equations with constant coefficients and commensurate time lags
Saiei-Jaeyeong Matsubara-Heo
We introduce the ring of partial differential operators with constant coefficients and commensurate time lags (we use the terminology D operators from now) initially defined by…