Related papers: Totally non congruence Veech groups

We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving…

We introduce a class of objects which we call 'affine surfaces'. These provide families of foliations on surfaces whose dynamics we are interested in. We present and analyze a couple of examples, and we define concepts related to these in…

We construct an explicit family of finite-area, infinite-genus translation surfaces whose vertical translation flow is strongly mixing. This provides a positive answer to a question posed by Lindsey and Trevi\~no~\cite{LT}

A linear group G on a finite vector space V, (that is, a subgroup of GL(V)) is called (1/2)-transitive if all the G-orbits on the set of nonzero vectors have the same size. We complete the classification of all the (1/2)-transitive linear…

In the present note, we complete the correspondence between stratum components of translation surfaces in low genus and finite-type Artin groups with defining Dynkin diagram containing $E_6$. In an earlier work, we showed that in genus $3$…

In this paper we are interested in the stratum H^{hyp}(4) of translation surfaces, which consists of pairs (M,\omega), where M is a hyper-elliptic Riemann surface of genus 3, and \omega is a holopmorphic 1-form on M having only one zero. We…

A non-square-tiled Veech surface has finitely many periodic points, i.e., points with finite orbit under the affine automorphism group. We present an algorithm that inputs a non-square-tiled Veech surface and outputs its set of periodic…

Let $\AAutH (X)$ be the subgroup of the group $\AutH (X)$ of holomorphic automorphisms of a normal affine algebraic surface $X$ generated by elements of flows associated with complete algebraic vector fields. Our main result is a…

We classify $\text{GL}(2,\mathbb{R})$ orbit closures in the product of strata of translation surfaces. Applications exist to joinings of certain Masur-Veech measures.

Structure theorems for exceptional objects and exceptional collections of the bounded derived category of coherent sheaves on del Pezzo surfaces are established by Kuleshov and Orlov. In this paper we propose conjectures which generalize…

In this paper we consider the symmetries of triangulable half-dilation structures on the sphere with four singularities. We show that all such surfaces can be produced by a tetrahedral construction. Using this construction, we calculate…

The genus spectrum of a finite group $G$ is the set of all $g\geq 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating the…

There is a natural action of SL(2,R) on the moduli space of translation surfaces, and this yields an action of the unipotent subgroup $U = {\begin{pmatrix} 1 & * 0 & 1 \end{pmatrix}}$. We classify the U-invariant ergodic measures on certain…

The family of translation surfaces $(X_g,\omega_g)$ constructed by Arnoux and Yoccoz from self-similar interval exchange maps encompasses one example from each genus $g$ greater than or equal to $3$. We triangulate these surfaces and deduce…

Veech groups uniformize Teichm\"uller geodesic curves in Riemann moduli space. Recently, examples of infinitely generated Veech groups have been given. We show that these can even have infinitely many cusps and infinitely many infinite…

Though the uniformization theorem guarantees an equivalence of Riemann surfaces and smooth algebraic curves, moving between analytic and algebraic representations is inherently transcendental. Our analytic curves identify pairs of circles…

We express the Masur--Veech volumes of "completed" strata of quadratic differentials with only odd singularities as a sum over stable graphs. This formula generalizes the formula of Delecroix-Goujard-Zograf-Zorich for principal strata. The…

We give an example of a Teichm\"uller curve which contains, in a factor of its monodromy, a group which was not observed before. Namely, it has Zariski closure equal to the group $SO^*(6)$ in its standard representation; up to finite index,…

In this paper we review the theory of slope gap distributions of translation surfaces and summarize the state-of-the-art for calculating slope gap distributions of Veech surfaces. We then derive the slope gap distribution of a particular…

An oblivious point on a translation surface is a point with no closed geodesic passing through it. Nguyen, Pan, and Su (2017) showed that there are at most finitely many oblivious points on any given translation surface and constructed a…