4 papers
Quantum Stokes matrices and quantum Riemann-Hilbert-Birkhoff maps
Xiaomeng Xu
In this paper, we introduce quantum Stokes matrices for a noncommutative version of meromorphic linear systems of ordinary differential equations with 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 referred to as A-groups or reduced GLMY homotopy groups. Localizing the category of directed…
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…
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…