Mellin-Barnes integrals as Fourier-Mukai transforms

Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations

We establish a braid monodromy representation of functions satisfying an algebraic equation containing three terms (trinomial equation). We follow global analytic continuation of the roots to a trinomial algebraic equation that are expressed by Mellin-Barnes integral representations. We depict braids that arise from the monodromy around all branching points. The global braid monodromy is described in terms of rational twists of strands that yield a classical Artin braid representation of algebraic functions. As a corollary, we get a precise description of the Galois group of a trinomial algebr…

On parabolic Whittaker functions

We derive a Mellin-Barnes integral representation for solution to generalized (parabolic) quantum Toda lattice introduced in \cite{GLO}, which presumably describes the $(S^1\times U_N)$-equivariant Gromov-Witten invariants of Grassmann variety.

Monodromy of A-hypergeometric functions

Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system. This article is a major rewrite of an article posted 2 years ago.

环簇的量子 D-模与振荡积分

Quantum D-modules of toric varieties and oscillatory integrals

本文回顾了紧弱Fano环流形量子上同调D-模的镜像对称，并探讨了其与GKZ系统、Stanley-Reisner环、Mellin-Barnes积分及Gamma积分结构的关系。

簇堆叠包的crepant变换对应关系

Crepant Transformation Correspondence For Toric Stack Bundles

本文通过构造辛变换和 Fourier-Mukai 同构，研究了簇堆叠包在 crepant 墙交叉下的 Gromov-Witten 理论对应关系。