arXiv research

The natural automorphism group of a translation surface is its group of translations. For finite translation surfaces of genus g > 1 the order of this group is naturally bounded in terms of g due to a Riemann-Hurwitz formula argument. In analogy with classical Hurwitz surfaces, we call surfaces which achieve the maxima…

Unique minimal translation surfaces found in Heisenberg group.

Study of translators in solvable group, finding new examples and non-existence.

Classification of groups as symmetries of infinite translation surfaces.

Totally non congruence Veech groups found in translation surfaces.

A translation surface in the Heisenberg group $\mathrm{Nil}_3$ is a surface constructed by multiplying (using the group operation) two curves. We completely classify minimal translation surfaces in the Heisenberg group $\mathrm{Nil}_3$.

Finite groups can be automorphism groups of translation surfaces with poles.

Minimal translation lengths for Torelli and pure braid groups on curve graphs are shown.

Researchers classify invariant translating solitons in the Heisenberg group.

Study left invariant spray geometry on Lie groups using parallel translations.

Algorithm constructs surfaces with specific Veech groups in lattice strata.

Translation surfaces in Heisenberg group classified by Gauss map determinant.

It is known that Garside groups are strongly translation discrete. In this paper, we show that the translation numbers in a Garside group are rational with uniformly bounded denominators and can be computed in finite time. As an application, we give solutions to some group-theoretic problems.

Group-equivariant subsampling layers improve CNNs' equivariance.

The paper classifies and describes translators in $SL(2,\mathbb{R})$ under specific symmetry conditions.

New algorithm for computing Veech groups from translation surfaces.

New lattice extensions of Schottky groups in hyperbolic space.

The paper classifies invariant translators for a specific curvature flow.

We prove that there does not exist any connected topological proper loop homeomorphic to a quasi-simple Lie group and having a compact Lie group as the group topologically generated by its left translations. Moreover, any connected topological loop homeomorphic to the 7-sphere and having a compact Lie group as the grou…

Study classifies special surfaces in space with translational and rotational symmetries.

New geometric generalizations of subgroup containment found for Lie groups.

Study static Einstein-Maxwell space invariant by translation.

Introduces a natural parallel translation for navigation data.

Affine equivalence of half-translation surfaces via saddle connection graphs.

We study Veech groups of covering surfaces of primitive translation surfaces. Therefore we define congruence subgroups in Veech groups of primitive translation surfaces using their action on the homology with entries in $\mathbb{Z}/a\mathbb{Z}$. We introduce a congruence level definition and a property of a primitive t…

We prove that every finite subgroup of $GL_{2}(\mathbb{R})$ can be realized as the Veech group of some translation surface.

Two quasi-morphisms on disk symplectomorphisms linked to Poincaré's translation number.

We define an infinite series of translation coverings of Veech's double-n-gon for odd n greater or equal to 5 which share the same Veech group. Additionally we give an infinite series of translation coverings with constant Veech group of a regular n-gon for even n greater or equal to 8. These families give rise to expl…

Random walks on hyperbolic spaces show linear growth in translation lengths.

The paper classifies surfaces in the Heisenberg space invariant under specific isometries.

Study of polynomial strata using braid groups and translation surfaces.

Let $Γ$ be a finitely generated group and $G$ be a noncompact semisimple connected real Lie group with finite center. We consider the space $\mathcal X$ of conjugacy classes of reductive representations of $Γ$ into $G$. We define the {\it translation vector} of an element $g$ in $G$, with values in a Weyl chamber, as a…

Affirmative answer to flat holomorphic Cartan geometries on complex tori.

Study of translation covers of platonic solids reveals monodromy group structures.

Talked about the Veech group of a specific surface.

Affine diffeomorphisms are undistorted in half-translation surfaces.

New bound for group action length without diameter restriction.

This paper develops optimal transport methods on the roto-translation group SE2.

Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation when two elements $g,h$ in a free group $F$ have the property that for every free isometric action of $F$ on an $\mathbb{R}$-…

Study classifies minimal surfaces and solitons in hyperbolic 3-space as translation surfaces.

Study on finiteness property of right-angled Artin groups actions on extension graphs.

Study confirms non-injective monodromy for even genus 4 translation surfaces.

Researchers classify and describe $K^α$-translators in Euclidean space.

The study examines pseudo-Anosov maps on curve complexes and their asymptotic translation lengths.

New Lagrangian and special Lagrangian examples found in complex space.

Translates Benoist's work on homogeneous reductive spaces.

Criterion for periodic orbits convergence proved.

We characterize subgroups of the mapping class group that stabilize a Teichmueller disk in terms of ellipses and strips that are immersed in the associated translation surface. In particular, we show that the space of immersed ellipses/strips that meet at least three cone points is naturally a (non-manifold) 2-dimensio…