arXiv subjects

Gabriela Weitze-Schmithüsen

Publications and source records attributed to Gabriela Weitze-Schmithüsen.

5 recordsLinked to original sources

arXiv2026

Realizing groups as symmetries of infinite translation surfaces

We provide a complete classification of groups that can be realized as isometry groups of a translation surface $M$ with non-finitely generated fundamental group and no planar ends. Furthermore, we demonstrate that if $S$ has no non-displaceable subsurfaces and its space of ends is self-similar, then every countable subgroup of $\operatorname{GL}^+(2,\mathbb{R})$ can be realized as the Veech group of a translation surface $M$ homeomorphic to $S$. The latter result generalizes and improves upon the previous findings of Przytycki-Valdez-Weitze-Schmithüsen and Maluendas-Valdez. To prove these results, we adapt ideas from the work of Aougab-Patel-Vlamis, which focused on hyperbolic surfaces, to translation surfaces.

math.GT↗

arXiv2025

Veech groups of covers of the Chamanara surface

We study finite abelian covers of the Chamanara surface, an example of a finite-area infinite translation surface with interesting dynamics and a large Veech group. Specifically, the Veech group of the Chamanara surface is a virtually free group on two generators. We characterize when finite abelian covers have large Veech groups themselves, namely when their Veech group has finite index in that of the Chamanara surface. For degree-2 covers, we provide a detailed analysis of these finite-index Veech groups. As an application, we prove that every free group arises as the projective Veech group of a finite-area infinite translation surface.

math.GT↗

arXiv2024

Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces

The variations of Hodge structures of weight one associated to square-tiled surfaces naturally generate interesting subgroups of integral symplectic matrices called Kontsevich--Zorich monodromies. In this paper, we show that arithmetic groups are frequent among the Kontsevich--Zorich monodromies of square-tiled surfaces of low genera $g$.

math.DS↗

arXiv2022

Systolic geometry of translation surfaces

In this paper we investigate the systolic landscape of translation surfaces for fixed genus and fixed angles of their cone points. We furthermore study how the systoles of a translation surface relate to the systoles of its graph of saddle connections. This allows us to develop an algorithm to compute the systolic ratio of origamis in the stratum $\mathcal{H}(1,1)$. We compute the maximal systolic ratio of all origamis in $\mathcal{H}(1,1)$ with up to 67 squares. These computations support a conjecture of Judge and Parlier about the maximal systolic ratio in $\mathcal{H}(1,1)$.

math.GT↗

arXiv2012

Explicit Teichmüller curves with complemetary series

We construct an explicit family of arithmetic Teichmüller curves $\mathcal{C}_{2k}$, $k\in\mathbb{N}$, supporting $\textrm{SL}(2,\mathbb{R})$-invariant probabilities $μ_{2k}$ such that the associated $\textrm{SL}(2,\mathbb{R})$-representation on $L^2(\mathcal{C}_{2k}, μ_{2k})$ has complementary series for every $k\geq 3$. Actually, the size of the spectral gap along this family goes to zero. In particular, the Teichmüller geodesic flow restricted to these explicit arithmetic Teichmüller curves $\mathcal{C}_{2k}$ has arbitrarily slow rate of exponential mixing.

math.DS↗