Related papers: Relatively Anosov representations via flows I: the…

We explore the potential of a formulation of the Navier-Stokes equations incorporating a random description of the small-scale velocity component. This model, established from a version of the Reynolds transport theorem adapted to a…

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the…

Let $\Gamma$ be a surface group of higher genus. Let $\rho\_0: \Gamma \to {PGL}(V)$ be a discrete faithful representation with image contained in the natural embedding of ${SL}(2, {\mathbb R})$ in ${PGL}(3, {\mathbb R})$ as a group…

This paper is devoted to rigidity of smooth bundles which are equipped with fiberwise geometric or dynamical structure. We show that the fiberwise associated sphere bundle to a bundle whose leaves are equipped with (continuously varying)…

We present a careful approximation of the geodesics in trees of hyperbolic or relatively hyperbolic groups. As an application we prove a combination theorem for finite graphs of relatively hyperbolic groups, with both Farb's and Gromov's…

Taking only the characteristics as absolute, in the spirit of Arnold's "Geometrical Methods in the Theory of Ordinary Differential Equations" (Springer, 1988), we give an independent of coordinates formulation of general variational entropy…

Flow past a line vortex in a simple perfect fluid or superfluid gives rise to a transverse Magnus force that is given by the well known Joukowski lift formula. The problem of generalising this to multiconstituent superfluid models has been…

We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include regularity results for Manhattan curves, the uniqueness of…

Let $\Gamma$ be a finitely generated group, and let $\op{Rep}(\Gamma, \SO(2,n))$ be the moduli space of representations of $\Gamma$ into $\SO(2,n)$ ($n \geq 2$). An element $\rho: \Gamma \to \SO(2,n)$ of $\op{Rep}(\Gamma, \SO(2,n))$ is…

This paper introduces a novel mathematical framework for examining the regularity and energy dissipation properties of solutions to the stochastic Navier-Stokes equations. By integrating Sobolev-Besov hybrid spaces, fractional differential…

In this paper, we describe a new approach to the problem of classification of transitive Anosov flows on 3-manifolds up to orbital equivalence. More specifically, generalizing the notion of Markov partition, we introduce the notion of…

This paper shows that every Gromov hyperbolic group can be described by a finite subdivision rule acting on the 3-sphere. This gives a boundary-like sequence of increasingly refined finite cell complexes which carry all quasi-isometry…

In this paper we describe multigraded generalizations of some constructions useful for mathematical understanding of gauge theories: we perform a near-at-hand generalization of the Aleksandrov--Kontsevich--Schwarz--Zaboronsky procedure, we…

Bifoliated planes arise naturally in the study of Anosov flows on $3$-manifolds. To any Anosov flow on a $3$-manifold $M$, one can associate a bifoliated plane equipped with an action of the fundamental group of $M$ which encodes the…

We study the topology and geometry of compact complex manifolds associated to Anosov representations of surface groups and other hyperbolic groups in a complex semisimple Lie group $G$. These manifolds are obtained as quotients of the…

Given an Anosov representation $\rho \colon \pi_1(S) \to \PSL_{n}(\mathbb{R})$ and a maximal geodesic lamination $\lambda$ in a surface $S$, we construct shear deformations along the leaves of the geodesic lamination $\lambda$ endowed with…

We develop a description of higher gauge theory with higher groupoids as gauge structure from first principles. This approach captures ordinary gauge theories and gauged sigma models as well as their categorifications on a very general…

We take a first step towards understanding the relationship between foliations and universally tight contact structures on hyperbolic 3-manifolds. If a surface bundle over a circle has pseudo-Anosov holonomy, we obtain a classification of…

Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and…

In studies of bundled modalities, we encode a complex conceptual notion into the semantics of a single modal operator and study its logic. Although there is already a substantial body of work on various concrete bundled operators, we still…