Related papers: On unipotent flows in H(1,1)

We compute the weighted Euler characteristic, equivariant with respect to the action of the symplectic group of degree six over the field of two elements, of the moduli space of principally polarized abelian threefolds together with a level…

In a previous paper we showed that for every polarization on an abelian variety there is a dual polarization on the dual abelian variety. In this note we extend this notion of duality to families of polarized abelian varieties. As a main…

We study universal families of stable genus two curves with level structure. Among other things, it is shown that the (1,1) part is spanned by divisor classes, and that there are no cycles of type (2,2) in the third cohomology of the first…

We provide a new proof that the horocycle flow preserving the Margulis measure on a variable negative curvature surface is standard. This was first proved by Ratner. The main purpose of this note is to provide a simplified case of the…

The purpose of this paper is to study transport equations on the unit tangent bundle of closed oriented Riemannian surfaces and to connect these to the transport twistor space of the surface (a complex surface naturally tailored to the…

We study the monodromy of the Hitchin fibration for moduli spaces of parabolic G-Higgs bundles in the cases when G=SL(2,R), GL(2,R) and PGL(2,R) A calculation of the orbits of the monodromy with Z2-coefficients provides an exact count of…

Let $O_F$ be the ring of integers of a totally real field $F$ of degree $g$. We study the reduction of the moduli space of separably polarized abelian $O_F$-varieties of dimension $g$ modulo $p$ for a fixed prime $p$. The invariants and…

We prove that the geodesic flow for the Weil-Petersson metric on the moduli space of Riemann surfaces is ergodic (in fact Bernoulli) and has finite, positive metric entropy.

We investigate the harmonic map heat flow from a compact Riemannian manifold \( M \) into the moduli space \( \mathcal{M}_1 \) of unit-area flat tori, which carries a natural hyperbolic structure as the quotient \( \mathrm{SL}(2,\mathbb{Z})…

This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…

Let $\mathcal{C}$ be a connected component of a stratum of the moduli space of holomorphic $1$-forms of genus $g$. We show that the absolute period foliation of $\mathcal{C}$ is ergodic on the area-$1$ locus, and that the non-dense leaves…

We prove measure rigidity for the action of (maximal) horospherical subgroups on homogeneous spaces obtained by quotient by a uniform (nonuniform) arithmetic lattices over a field of positive characteristic.

We consider the dynamical system given by a diagonalizable element $a$ of a closed linear unimodular algebraic subgroup $G$ of the special linear group over the $p$-adic numbers acting by translation on a finite volume quotient $X$.…

We prove bounds for twisted ergodic averages for horocycle flows of hyperbolic surfaces, both in the compact and in the non-compact finite area case. From these bounds we derive effective equidistribution results for horocycle maps. As an…

We study the integral, rational, and modular Alexander invariants, as well as the cohomology jump loci of groups arising as extensions with trivial algebraic monodromy. Our focus is on extensions of the form $1\to K\to G\to Q\to 1$, where…

Let Q be a connected component of a stratum in the space of quadratic differentials for a non-exceptional Riemann surface of finite type. We show that the probability measure on Q in the Lebesgue measure class which is invariant under the…

Let $E$ be a subset of positive integers such that $E\cap\{1,2\}\ne\emptyset$. A weakly mixing finite measure preserving flow $T=(T_t)_{t\in\Bbb R}$ is constructed such that the set of spectral multiplicities (of the corresponding Koopman…

We study the symplectic geometry of the SU(2)-representation variety of the compact oriented surface of genus 2. We use the Goldman flows to identify subsets of the moduli space with corresponding subsets of $\mathbb P^3(\mathbb C)$. We…

We identify a class of hyperbolic transcendental entire maps and we prove that some of its elements generate a class of potentials for which exhibit a conformal and invariant probability Gibbs measure. The methods and techniques from the…

The algebraic entropy h, defined for endomorphisms f of abelian groups G, measures the growth of the trajectories of non-empty finite subsets F of G with respect to f. We show that this growth can be either polynomial or exponential. The…