Related papers: Canonical translation surfaces for computing Veech…

Consider a lattice in a real finite dimensional vector space. Here, we are interested in the lattice polytopes, that is the convex hulls of finite subsets of the lattice. Consider the group $G$ of the affine real transformations which map…

Extending the results of [Asian J. Math. 2019], in [Doc. Math. \textbf{21}, 2016] we calculated explicitly the number of isomorphism classes of superspecial abelian surfaces over an arbitrary finite field of \textit{odd} degree over the…

We prove that a ``bouillabaisse'' surface (translation surface which has two transverse parabolic elements) has totally real trace field. As a corollary, non trivial Veech groups which have no parabolic elements do exist. The proof follows…

We study Lagrange spectra of Veech translation surfaces, which are a generalization of the classical Lagrange spectrum. We show that any such Lagrange spectrum contains a Hall ray. As a main tool, we use the boundary expansion developed by…

This text presents a scheme-theoretic enhancement of the theory of smooth profinite groups and cyclotomic pairs, introduced in the paper `Smooth profinite groups, I'. To do so, our main technical tools are Hochschild cohomology of affine…

We study the Picard groups of connected linear algebraic groups, and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every global function field. We also utilize our study of these…

The (in)finite dimensional symplectic group of homogeneous canonical transformations is represented on the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states.

Weingarten transformations which, by definition, preserve the asymptotic lines on smooth surfaces have been studied extensively in classical differential geometry and also play an important role in connection with the modern geometric…

A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D\subseteq X$ and a morphism $\Lambda^{2}E\rightarrow\mathcal{O}_{X}$ satisfying some additional…

We give a topological interpretation of the core group invariant of a surface embedded in S^4. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover of S^4 with the surface as a…

We present an algorithm that computes Bowditch's canonical JSJ decomposition of a given one-ended hyperbolic group over its virtually cyclic subgroups. The algorithm works by identifying topological features in the boundary of the group. As…

In the homogeneous space Sol$_3$, a translation surface is parameterized by $x(s,t)=\alpha(s)\ast\beta(t)$, where $\alpha$ and $\beta$ are curves contained in coordinate planes and $\ast$ denotes the group operation of Sol$_3$. In this…

In this article we show that for any given Riemann surface $\Sigma$ of genus $g$, we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at infinity conformal to $\Sigma$ in terms of the genus and…

In this note, we explore the notion of hyperbolicity of topologically finitely generated profinite groups. Some applications to diophantine geometry are suggested and we try to reformulate certain problems in diophantine geometry in terms…

We prove the existence of Veech groups having a critical exponent strictly greater than any elementary Fuchsian group (i.e. $>\frac{1}{2}$) but strictly smaller than any lattice (i.e. $<1$). More precisely, every affine covering of a…

We aim to give a strict proof of the existence and uniqueness of the weighted Voronoi decomposition and the dual weighted Delaunay triangulation on Euclidean and hyperbolic polyhedral surface as well as hyperbolic surface with geodesic…

In this paper, we introduce the notion of "geodesic cover" for Fuchsian groups, which summons copies of fundamental polygons in the hyperbolic plane to cover pairs of representatives realizing distances in the corresponding hyperbolic…

The goal of this work is to give new quantitative results about the distribution of semi-arithmetic hyperbolic surfaces in the moduli space of closed hyperbolic surfaces. We show that two coverings of genus $g$ of a fixed arithmetic surface…

In this paper we study the regularized analytic torsion of finite volume hyperbolic manifolds. We consider sequences of coverings $X_i$ of a fixed hyperbolic orbifold $X_0$. Our main result is that for certain sequences of coverings and…

We generalise to the genus one case several results of Thurston concerning moduli spaces of flat Euclidean structures with conical singularities on the two dimensional sphere. More precisely, we study the moduli space of flat tori with $n$…