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Distribution of shapes of orthogonal lattices
It was recently shown by Aka, Einsiedler and Shapira that if d>2, the set of primitive vectors on large spheres when projected to the d-1-dimensional sphere coupled with the shape of the lattice inExpand
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Effectivity of Uniqueness of the Maximal Entropy Measure on $p$-adic homogeneous spaces
We consider the dynamical system given by an Ad-diagonalizable element a of the Qp-points G of a unimodular linear algebraic group acting by translation on a finite volume quotient X . Assuming thatExpand
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Pressure Inequalities for Gibbs Measures of Countable Markov Shifts
X = {x = (x0, x1, . . . ) ∈ S0 : txixj = 1} for a countable sets of states S, A = (tij)i,j∈S denotes the transition matrix and T : X → X is the left shift, which we assume to be topologically mixing.Expand
Effective counting on translation surfaces
We prove an effective version of a celebrated result of Eskin and Masur: for any affine invariant manifold of translation surfaces, almost every translation surface has quadratic growth for theExpand
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Metric Diophantine approximation with congruence conditions
We prove a version of the Khinchine--Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani correspondence to theExpand
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Effective counting for discrete lattice orbits in the plane via Eisenstein series
We prove effective bounds on the rate in the quadratic growth asymptotics for the orbit of a non-uniform lattice of SL(2,R), acting linearly on the plane. This gives an error bound in the count ofExpand
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Counting saddle connections in a homology class modulo $q$
We give effective estimates for the number of saddle connections on a translation surface that have length $\leq L$ and are in a prescribed homology class modulo $q$. Our estimates apply to almostExpand
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A Convexity Criterion for Unique Ergodicity of Interval Exchange Transformations
There is a meta-conjecture in metric number theory that states that any Diophantine property that holds for generic vectors in R should hold for generic vectors on nondegenerate subvarities, seeExpand
Quantitative Multiple pointwise convergence and effective multiple correlations
We show that effective $2\ell$-multiple correlations imply quantitative $\ell$-multiple pointwise ergodic theorems. The result has a wide class of applications which include subgroup actions onExpand
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Classification and statistics of cut and project sets
We define Ratner-Marklof-Strömbergsson measures (following [MS14]). These are probability measures supported on cutand-project sets in R pd ě 2q which are invariant and ergodic for the action of theExpand