We review the different notions of translation surfaces that are necessary to understand
McMullen's classification of GL 2+(ℝ)-orbit closures in genus two. We start by recalling the …

We give an explicit formula for the limiting gap distribution of slopes of saddle connections
on the golden L, or any translation surface in its SL (2, R)-orbit, in particular the double …

We give a tree structure on the set of all periodic directions on the golden L, which gives an
associated tree structure on the set of periodic directions for the pentagon billiard table and …

We describe the cutting sequences associated to geodesic flow on regular polygons, in
terms of a combinatorial process called derivation. This work is an extension of some of the …

We consider flow directions on the translation surfaces formed from double $(2n+ 1) $-gons,
and give a sufficient condition in terms of a natural gcd algorithm for a direction to be …

We consider the relations between the lengths of periodic billiard trajectories in regular
triangles, squares, and regular pentagons and those of closed geodesics on the surfaces of …

We consider a symbolic coding for geodesics on the family of Veech surfaces (translation
surfaces rich with affine symmetries) recently discovered by Bouw and Moeller. These …

We study the function $$\mbox {KVol}:(X,\omega)\mapsto\mbox {Vol}(X,\omega)\sup_
{\alpha,\beta}\frac {\mbox {Int}(\alpha,\beta)}{l_g (\alpha) l_g (\beta)} $$ defined on the …

We analyze the cutting sequences associated to geodesic flow on a large class of
translation surfaces, including Bouw-Moller surfaces. We give a combinatorial rule that …

arxiv:2409.10682v1 [math.NT] 16 Sep 2024 Page 1 ON THE LOCAL-GLOBAL CONJECTURE
FOR COMBINATORIAL PERIOD LENGTHS OF CLOSED BILLIARDS ON THE REGULAR …