Related papers: The lattice points of a stacky polytope
We construct relative moduli spaces of semistable pairs on a family of projective Deligne-Mumford stacks. We define moduli stacks of stable orbifold Pandharipande-Thomas pairs on stacks of expanded degenerations and pairs, and then show…
We study prismatics sets analogously to simplical sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set S and the…
We study the stratification of the singular locus of four dimensional $\mathcal{N}=2$ Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant…
Higher bundles are homotopy coherent generalisations of classical fibre bundles. They appear in numerous contexts in geometry, topology and physics. In particular, higher principal bundles provide the geometric framework for higher-group…
This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about…
The shape of the cross section of a dense fiber bundle is related to the symmetry of its molecular packing. However, this statement might be belied by type I collagen fibrils which have a rounded section of high symmetry while structural…
An explicit construction of a pre-quantum line bundle for the moduli space of flat G-bundles over a Riemann surface is given, where G is any non-simply connected compact simple Lie group. This work helps to explain a curious coincidence…
In this paper, we compute the Stokes matrices of a special quantum confluent hypergeometric system with Poincar\'e rank one. The sources of the interests in the Stokes phenomenon of such system are from representation theory and the theory…
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.
The theory of polyptych lattices is a framework to obtain a family of toric degenerations whose polytopes are related by piecewise-linear transformations. It can be regarded as a generalization of toric degenerations arising from cluster…
We define the moduli problem of Hitchin pairs over Deligne-Mumford Stack and prove this moduli problem is represented by a separated and locally finitely presented algebraic space, which is considered as the moduli space of Hitchin pairs…
We give a parametrization for crystal bases of Demazure modules as a set of lattice points in some convex polytope and we also describe explicitly the extremal vectors as solutions of some system of linear equations.
The below discussion is in three sections A, B, C, each section in two parts I, II, I representing the standpoint of bundles with connections and II representing the standpoint of prehomogeneous geometries (phg's). In A, our object of study…
We examine the stationary--state equations for lattices with generalized Markovian dephasing and relaxation. When the Hamiltonian is quadratic, the single--particle correlation matrix has a closed system of equations even in the presence of…
We investigate in this paper the relation between Apollonian $d$-ball packings and stacked $(d+1)$-polytopes for dimension $d\ge 3$. For $d=3$, the relation is fully described: we prove that the $1$-skeleton of a stacked $4$-polytope is the…
We introduce a collection of convex polytopes associated to a torus-equivariant vector bundle on a smooth complete toric variety. We show that the lattice points in these polytopes correspond to generators for the space of global sections…
This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between…
In this paper we prequantize the moduli space of non-abelian vortices. We explicitly calculate the symplectic form arising from the $L^2$ metric and we construct a prequantum line bundle whose curvature is proportional to this symplectic…
This is a continuation of the early paper concerning matroid base polytope decomposition. Here, we will present sufficient conditions on $M$ so its base matroid polytope $P(M)$ has a {\em sequence} of hyperplane splits. The latter yields to…
This article is devoted to the study of the centralizer and the clifforder of a matrix over a field $\mathbb{F}$ of characteristic zero, as well as the quasi-commutative relations between matrices over the complex field $\mathbb{C}$. We…