Related papers: On a group associated to $z^2-1$
Let $J$ be the Jacobian of a smooth projective curve. We define a natural action of the Lie algebra of polynomial Hamiltonian vector fields on the plane, vanishing at the origin, on the Chow group of $J$ with rational coefficients. Using…
We consider a large class of so-called dynamical Belyi maps and study the Galois groups of iterates of such maps. From the combinatorial invariants of the maps, we construct a useful presentation of their Galois groups as subgroups of…
We introduce the discrete affine group of a regular tree as a finitely generated subgroup of the affine group. We describe the Poisson boundary of random walks on it as a space of configurations. We compute isoperimetric profile and Hilbert…
Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on…
We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
We leverage a correspondence between group actions and edge-labelled graphs in two ways. First, we give a unified presentation of several folklore results connecting weak containment, local-global convergence, and continuous model theory.…
Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…
This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric-functional boundary. We show that, if there exists a Cayley graph with finitely many Busemann points, then the…
The a-adic numbers are those groups that arise as Hausdorff completions of noncyclic subgroups of the rational numbers. We give a crossed product construction of (stabilized) Cuntz-Li algebras coming from the a-adic numbers and investigate…
Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least…
We construct a model for the space of automorphisms of a connected p-compact group in terms of the space of automorphisms of its maximal torus normalizer and its root datum. As a consequence we show that any homomorphism to the outer…
Many previously studied path algebras or self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid…
We study the arithmetic of curves and Jacobians endowed with the action of a finite group $G$. This includes a study of the basic properties, as $G$-modules, of their $\ell$-adic representations, Selmer groups, rational points and…
We use the theory of cubic structures to give a fixed point Riemann-Roch formula for the equivariant Euler characteristics of coherent sheaves on projective flat schemes over Z with a tame action of a finite abelian group. This formula…
We consider the dynamics of rational semigroups (semigroups of rational maps) on the Riemann sphere. We provide proof that a random backward iteration algorithm to draw the pictures of the Julia sets, previously proven to work in the…
A new universal model to implement the Seiberg-Witten approach to low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It is based on the…
The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. In particular, we discuss some important totally geodesic…
The semidirect product of a finitely generated group dual with the symmetric group can be described through so-called group-theoretical categories of partitions (covers only a special case; due to Raum--Weber, 2015) and skew categories of…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…