19 citations · 69 across the 21 of their papers we have counts for
21 papers
Quantum Stokes matrices and quantum Riemann-Hilbert-Birkhoff maps
Xiaomeng Xu
In this paper, we define quantum Stokes matrices of meromorphic linear systems of ordinary differential equations with noncommutative coefficients and a pole of order . We pro…
The discrete homotopy hypothesis for directed graphs
Briony Eldridge, Sergei O. Ivanov, Xiaomeng Xu +2
We develop a homotopy theory of directed graphs based on cubical homotopy groups, also known as -groups or reduced GLMY homotopy groups. Localizing the category of directed grap…
On the connection formula of a higher rank analog of Painlevé VI
Xiaomeng Xu
In this paper, we derive the connection formula for the higher rank analog of Painlevé VI arising from the isomonodromic deformation theory and the study of Frobenius manifolds.
WKB approximation, crystals and combinatorics of Young tableaux
Xiaomeng Xu
In this paper, we show how various combinatorial algorithms of Young tableaux naturally arise from the WKB approximation of the connection matrix of quantum confluent hypergeometri…
Stokes phenomenon and reflection equations
Xiaomeng Xu
In this paper, we study the Stokes phenomenon of the cyclotomic Knizhnik-Zamolodchikov equation, and prove that its two types of Stokes matrices satisfy the Yang-Baxter and reflect…
Regularized limits of Stokes matrices, isomonodromy deformation and crystal basis
Xiaomeng Xu
In the first part of the paper, we solve the boundary and monodromy problems for the isomonodromy equation of the meromorphic linear system of ordinary differential equ…
Quasi-Invariants in Characteristic and Twisted Quasi-Invariants
Michael Ren, Xiaomeng Xu
The spaces of quasi-invariant polynomials were introduced by Chalykh and Veselov [Comm. Math. Phys. 126 (1990), 597-611]. Their Hilbert series over fields of characteristic 0 were…
Stokes phenomenon and Yang-Baxter equations
Xiaomeng Xu
We describe the monodromy of dynamical Knizhnik-Zamolodchikov equations via Stokes phenomenon. It defines a family of braid groups representations by certain Stokes matrices. In pa…
Frobenius manifolds and quantum groups
Xiaomeng Xu
We introduce isomonodromy Knizhnik-Zamolodchikov (KZ) connections with respect to the quantum Stokes matrices, and prove that the classical limit of the KZ type connections gives r…
Chern-Simons, Wess-Zumino and other cocycles from Kashiwara-Vergne and associators
Anton Alekseev, Florian Naef, Xiaomeng Xu +1
Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g. in the Chern-Simons field theory and in the theo…
Stokes phenomenon, Gelfand-Zeitlin systems and relative Ginzburg-Weinstein linearization
Xiaomeng Xu
In 2007, Alekseev-Meinrenken proved that there exists a Ginzburg-Weinstein diffeomorphism from the dual Lie algebra to the dual Poisson Lie group compatible…
String principal bundles and Courant algebroids
Yunhe Sheng, Xiaomeng Xu, Chenchang Zhu
Just like Atiyah Lie algebroids encode the infinitesimal symmetries of principal bundles, exact Courant algebroids are believed to encode the infinitesimal symmetries of -gerb…
Irregular Riemann-Hilbert correspondence, Alekseev-Meinrenken dynamical r-matrices and Drinfeld twists
Xiaomeng Xu
In 2004, Enriquez-Etingof-Marshall suggested a new approach to the Ginzburg-Weinstein linearization theorem for a quasitriangular Lie bialgebra $(\g,r)$. This approach is based on…
Generalized classical dynamical Yang-Baxter equations and moduli spaces of flat connections on surfaces
Xiaomeng Xu
In this paper, we explain how generalized dynamical r-matrices can be obtained by (quasi-)Poisson reduction. New examples of Poisson structures and Poisson groupoid actions natural…
Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids
Honglei Lang, Yunhe Sheng, Xiaomeng Xu
We study Maurer-Cartan elements on homotopy Poisson manifolds of degree . They unify many twisted or homotopy structures in Poisson geometry and mathematical physics, such as tw…
Current algebras from QP-manifolds in general dimensions
Noriaki Ikeda, Xiaomeng Xu
We propose a new unified formulation of the current algebra theory in general dimensions in terms of supergeometry. We take a QP-manifold, i.e. a differential graded (dg) symplecti…
Canonical Functions and Differential Graded Symplectic Pairs in Supergeometry and AKSZ Sigma Models with Boundary
Noriaki Ikeda, Xiaomeng Xu
Consistent boundary conditions for Alexandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) sigma models and the corresponding boundary theories are analyzed. As their mathematical structu…
Cohomology for almost Lie algebroids
Melchior Grützmann, Xiaomeng Xu
We give numerous examples of almost Lie algebroids arising as Dirac structures in pre-Courant algebroids, e.g. from twisted Poisson structures, as well as from twisted actions of a…
Twisted Courant algebroids and coisotropic Cartan geometries
Xu Xiaomeng
In this paper, we show that associated to any coisotropic Cartan geometry there is a twisted Courant algebroid. This includes in particular parabolic geometries. Using this twisted…
The Pontryagin Class for Pre-Courant Algebroids
Zhangju Liu, Yunhe Sheng, Xiaomeng Xu
In this paper, we show that the Jacobiator of a pre-Courant algebroid is closed naturally. The corresponding equivalence class is defined as the Pontryagin class, w…
Dirac and Generalized Complex Structures on Cartan Geometries
Honglei Lang, Xiaomeng Xu
We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on…