Related papers: Lagrange Spectra in Teichm\"uller Dynamics via ren…
In this note we show that the transfer operator of a Rauzy-Veech-Zorich renormalization map acting on a space of quasi-H\"older functions is quasicompact and derive certain statistical recurrence properties for this map and its associated…
Generalizing the well-known construction of Eisenstein series on the modular curves, Siegel-Veech transforms provide a natural construction of square-integrable functions on strata of differentials on Riemannian surfaces. This space carries…
We reduce a question of Eskin-Kontsevich-Zorich and Forni-Matheus-Zorich, which asks for a classification of all $\text{SL}_2(\mathbb{R})$-invariant ergodic probability measures with completely degenerate Kontsevich-Zorich spectrum, to a…
A stretched-exponential bound is obtained for the decay of correlations of the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations. A Corollary is the Central Limit Theorem for the Teichmueller flow on the…
We generalize a new class of cluster type mutations for which exchange transformations are given by reciprocal polynomials. In the case of second-order polynomials of the form $x+2\cos{\pi/n_o}+x^{-1}$ these transformations are related to…
We show that for any weakly convergent sequence of ergodic $SL_2(\mathbb{R})$-invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siegel-Veech constants converge to the Siegel-Veech constant of…
For a non-uniform lattice in SL(2,R), we consider excursions in cusp neighborhoods of a random geodesic on the corresponding finite area hyperbolic surface or orbifold. We prove a strong law for a certain partial sum involving these…
In this paper, we compare two definitions of Rauzy classes. The first one was introduced by Rauzy and was in particular used by Veech to prove the ergodicity of the Teichm\"uller flow. The second one is more recent and uses a "labeling" of…
The behavior near the boundary in the Deligne-Mumford compactification of many functions on the moduli space of pointed Riemann surfaces can be conveniently expressed using the notion of "point-like limit" that we adopt from the string…
In this article, we study the Zariski closure of modular points in the two-dimensional universal deformation space when the residual Galois representation is reducible. Unlike the previous approaches in the residually irreducible case from…
We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces, we prove that some classical linear operators such as Calder\'on-Zygmund,…
We investigate specific examples of locally-defined real vector-fields on strata of translation surfaces. Integrating SL(2,R)-loci of Veech surfaces along these vector-fields yield interesting new examples of horocyle-invariant ergodic…
We construct an Ahlfors-Bers complex analytic model for the Teichm\"uller space of the universal hyperbolic lamination (also known as Sullivan's Teichm\"uller space) and the renormalized Weil-Petersson metric on it as an extension of the…
We use spectral invariants in Lagrangian Floer theory in order to show that there exist \emph{isometric} embeddings of normed linear spaces (finite or infinite dimensional, depending on the case) into the space of Hamiltonian deformations…
Let X_0 be a compact connected Riemann surface of genus g with D_0\subset X_0 an ordered subset of cardinality n, and let E_G be a holomorphic principal G-bundle on X_0, where G is a complex reductive affine algebraic group, that admits a…
We prove that the restriction map from the subspace of regular points of the holonomy perturbed SU(2) traceless flat moduli space of a tangle in a 3-manifold to the traceless flat moduli space of its boundary marked surface is a Lagrangian…
We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the DeGeorge--Wallach Theorem, of a theorem of Delorme and…
We establish a formula for the spectral flow of a smooth family of twisted Dirac operators on a closed odd-dimensional Riemannian spin manifold, generalizing a result by Getzler. The spectral flow is expressed in terms of the $\hat{A}$-form…
Ten years ago A. Zorich discovered, by computer experiments on interval exchange transformations, some striking new power laws for the ergodic integrals of generic non-exact Hamiltonian flows on higher genus surfaces. In Zorich's later work…
We construct explicit closed GL(2, R)-invariant loci in strata of meromorphic differentials of arbitrary large dimension with fully degenerate Lyapunov spectrum. This answers a question of Forni-Matheus-Zorich.