Related papers: MV Polytopes and Masures

Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characterizes paths almost uniquely. We study truncations of this…

We define a notion of coordinatization for $\aleph_0$-categorical structures which is, like Lie coordinatized structures in [2], a certain kind of expansion of a tree. We show that a structure which is coordinatized, in a certain strong…

For a certain class of simple integrable modules of level zero over a quantised affine algebra, we establish the existence of a pseudo-crystal basis and show that such a basis admits a combinatorial realisation in the framework of the path…

A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In the contravariant case, the only such valuations are…

In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny…

In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but…

The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…

We continue development of the theory of contractive Markov systems initiated in \cite{Wer1}. In this paper, we construct the coding map for Feller contractive Markov systems. This allows us to prove a generalization of Ledrappier's Theorem…

Wythoff's construction associates a uniform polytope to a Coxeter diagram whose vertices are decorated with crosses, which indicate the subgroup stabilizing a generic point. Champagne, Kjiri, Patera, and Sharp remarked that by associating…

An orbit polytope is the convex hull of an orbit under a finite group $G \leq \operatorname{GL}(d,\mathbb{R})$. We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense…

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…

This paper follows from two earlier works. In the first we gave an explicit construction of opetopes, the underlying cell shapes in the theory of opetopic n-categories; at the heart of this construction is the use of certain trees. In the…

In this talk we report some results about the construction of soliton solutions for the Affine and Conformal Affine Toda models using the Hirota's method. We obtain new classes of solitons connected to the degeneracies of the Cartan matrix…

We show that the moduli space of regular affine vortices, which are solutions of the symplectic vortex equation over the complex plane, has the structure of a smooth manifold. The construction uses Ziltener's Fredholm theory results [31].…

Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…

Our rigorous path integrals costruction for the evolution operators is extended to metric-affine manifolds.

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable…

The diagonalisation of the transfer matrices of solvable vertex models with alternating spins is given. The crystal structure of (semi-)infinite tensor products of finite-dimensional $U_q(\hat{sl}_2)$ crystals with alternating dimensions is…

We settle two problems of reconstructing a biholomorphic type of a manifold. In the first problem we use graphs associated to Riemann surfaces of a particular class. In the second one we use the semigroup structure of analytic endomorphisms…

Motivated by the study of polytopes formed as the convex hull of permutation matrices and alternating sign matrices, we define several new families of polytopes as convex hulls of sign matrices, which are certain {0,1,-1}-matrices in…