Related papers: Atypical generic directions in Teichm\"uller space

We classify a natural collection of GL(2,R)-invariant subvarieties, which includes loci of double covers, the orbits of the Eierlegende-Wollmilchsau, Ornithorynque, and Matheus-Yoccoz surfaces, and loci appearing naturally in the study of…

A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well…

In this paper, we concern trace Trudinger-Moser inequalities on a compact Riemann surface with smooth boundary. This kind of inequalities were extensively studied by Osgood-Phillips-Sarnak [24], Liu [20], Li-Liu [17], Yang [31, 32] and…

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…

We continue the study of the geometry of infinite geodesics in first passage percolation (FPP) on Gromov-hyperbolic groups G, initiated by Benjamini-Tessera and developed further by the authors. It was shown earlier by the authors that,…

We define metrics on Culler-Vogtmann space, which are an analogue of the Teichmuller metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate…

Equivariant localization expresses global invariants in terms of local invariants, and many of them appearing in equivariant index theory, (holomorphic) Morse theory, geometric quantization and supersymmetric localization can be…

Geometric models and Teichm\"uller structures have been introduced for the space of smooth expanding circle endomorphisms and for the space of uniformly symmetric circle endomorphisms. The latter one is the completion of the previous one…

We prove several general conditional convergence results on ergodic averages for horocycle and geodesic subgroups of any continuous action of the Lie group SL(2, R) on a locally compact space. These results are motivated by theorems of…

We introduce a construction that gives rise to a variety of "geometric" finite random graphs, and describe connections to the Poisson boundary, Naim's kernel, and Sznitman's random interlacements.

An algebraic subvariety Z of A_g is totally geodesic if it is the image via the natural projection map of some totally geodesic submanifold X of the Siegel space. We say that X is the symmetric space uniformizing Z. In this paper we…

We study random walks on sub-Riemannian manifolds using the framework of retractions, i.e., approximations of normal geodesics. We show that such walks converge to the correct horizontal Brownian motion if normal geodesics are approximated…

We develop techniques that lay out a basis for generalizations of the famous Thurston's Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the…

Two people who pioneered the study of mapping class group-equivariant deformation retractions of Teichm\"uller space of closed compact surfaces are Schmutz Schaller and Thurston. This paper studies how the two different approaches are dual…

Let $q$ be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on $\mathbb F_q[x_1,\dots,x_m]$ combined with the ideas in (M. Datta and T. Johnsen, 2022). Compared with…

We prove a quantitative version of the non-uniform hyperbolicity of the Teichm\"uller geodesic flow. Namely, at each point of any Teichm\"uller flow line, we bound the infinitesimal spectral gap for variations of the Hodge norm along the…

In this note we present a simplified proof of the zero-one law by Merkl and Zerner (2001) for directional transience of random walks in i.i.d. random environments (RWRE) on the square lattice. Also, we indicate how to construct a…

We show that manifolds admitting special generic maps also admit nice generalized multisections. Special generic maps are natural generalized versions of Morse functions with exactly two singular points on closed manifolds, characterizing…

An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted…

Graph manifolds form important classes of $3$-dimensional closed and orientable manifolds. For example, {\it Seifert} manifolds are graph manifolds where hyperbolic manifolds are not. In applying singularity theory of differentiable maps to…