Related papers: Spatial Asymmetric Two dimensional Continuous Abel…
A version of non-Abelian monopole equations is explored through dimensional reductions, with often the addition of algebraic conditions. On zero curvature spaces, spinor related extensions of integrable systems have been generated, and…
We introduce a new lattice growth model, which we call boundary sandpile. The model amounts to potential-theoretic redistribution of a given initial mass on $\mathbb{Z}^d$ ($d\geq 2$) onto the boundary of an (a priori) unknown domain. The…
Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since…
We construct accidentally symmetric potentials in the framework of Two Higgs Model Effective Field Theory (2HDMEFT) including higher-order operators of dimension 6 and dimension 8. Our construction is facilitated by an earlier developed…
We extend to the topological setting the classical constructions of the Abel-Jacobi mapping on homologically trivial algebraic cycles and the height pairing between two such cycles. We further interpret the height pairing between…
The leaky abelian sandpile model (Leaky-ASM) is a growth model in which $n$ grains of sand start at the origin in $\mathbb{Z}^2$ and diffuse along the vertices according to a toppling rule. A site can topple if its amount of sand is above a…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
We study random tiling models in the limit of high rotational symmetry. In this limit a mean-field theory yields reasonable predictions for the configurational entropy of free boundary rhombus tilings in two dimensions. We base our…
We study the distribution of algebraic points on curves in abelian varieties over finite fields.
We introduce an asymptotic notion of positivity in algebraic geometry that turns out to be related to some high-dimensional convex sets. The dimension of the convex sets grows with the number of birational operations. In the case of complex…
We propose a unified approach to a general class of codimension-2 defects in field theories with non-trivial duality symmetries and discuss various constructions of such "duality defects" in diverse dimensions. In particular, in d=4 we…
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
We perform a high-accuracy moment analysis of the avalanche size, duration and area distribution of the Abelian Manna model on eight two-dimensional and four one-dimensional lattices. The results provide strong support to establish…
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a…
We give optimal estimates on the variation of the differential and modular heights within an isogeny class of abelian varieties defined over the function field of a curve (in any characteristic). We also prove a parallelogram inequality for…
Three dimensional topological field theories associated with the three dimensional version of Abelian and non-Abelian Seiberg-Witten monopoles are presented. These three dimensional monopole equations are obtained by a dimensional reduction…
Kinetic self-avoiding trails are introduced and used to generate a substrate of randomly quenched flow vectors. Sandpile model is studied on such a substrate with asymmetric toppling matrices where the precise balance between the net…
The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…
We analyse the global symmetry structure of two-dimensional Non-Linear Sigma Models with Wess-Zumino term. When the target space has a compact isometry without fixed points, the theory has a pair of (group-like) global symmetries and many…