Related papers: Twisted Translation Flows and Effective Weak Mixin…
In this paper, we study the existence of twisted constant scalar curvature K\"{a}hler (cscK) metrics and non-existence of coupled cscK metrics on minimal ruled surfaces over a Riemann surface of genus $2$. Moreover, we give a bound for the…
In the paper we introduce the notion of twisted derivation of a bialgebra. Twisted derivations appear as infinitesimal symmetries of the category of representations. More precisely they are infinitesimal versions of twisted automorphisms of…
We study Brownian flows on manifolds for which the associated Markov process is strongly mixing with respect to an invariant probability measure and for which the distance process for each pair of trajectories is a diffusion $r$. We provide…
Given a torus bundle $Y$ over the circle and a cohomology class $[\omega]\in H^2(Y;\mathbb{Z})$ which evaluates nontrivially on the fiber, we compute the Heegaard Floer homology of $Y$ with twisted coefficients in the universal Novikov…
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…
We explore an approach to twisted generalized cohomology from the point of view of stable homotopy theory and quasicategory theory provided by arXiv:0810.4535. We explain the relationship to the twisted K-theory provided by Fredholm…
This note is to concern a generalization to the case of twisted coefficients of the classical theory of Abelian differentials on a compact Riemann surface. We apply the Dirichlet's principle to a modified energy functional to show the…
We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted…
We develop a systematic functional-analytic framework for Hom--Lie Banach algebras, introducing bounded $\alpha$-twisted derivations and almost periodic elements. Under natural continuity and compactness assumptions, we establish a complete…
Abelian differentials on Riemann surfaces can be seen as translation surfaces, which are flat surfaces with cone-type singularities. Closed geodesics for the associated flat metrics form cylinders whose number under a given maximal length…
Twisted \'etale groupoid algebras have been studied recently in the algebraic setting by several authors in connection with an abstract theory of Cartan pairs of rings. In this paper, we show that extensions of ample groupoids correspond in…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
We study a diophantine property for translation surfaces, defined in term of saddle connections and inspired by the classical theorem of Khinchin. We prove that the same dichotomy holds as in Khinchin' result, then we deduce a sharp…
Twisted Morava K-theory, along with computational techniques, including a universal coefficient theorem and an Atiyah-Hirzebruch spectral sequence, was introduced by Craig Westerland and the first author. We employ these techniques to…
One of the most widespread canonical devices for fluid mixing is the T-shaped mixer, in which two opposing miscible liquid streams meet at a junction and then mix along a main channel. Laminar steady and time-periodic flows in T-shaped…
We develop the theory of twisted L^2-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on the first de Rham cohomology of M and they generalize the standard…
The main results of this paper are limit theorems for horocycle flows on compact surfaces of constant negative curvature. One of the main objects of the paper is a special family of horocycle-invariant finitely-additive Hoelder measures on…
We prove the Zorich-Kontsevich conjecture that the non-trivial Lyapunov exponents of the Teichm\"uller flow on (any connected component of a stratum of) the moduli space of Abelian differentials on compact Riemann surfaces are all distinct.…
In this thesis, we study the Teichm\"uller geodesic flow on the space of translation surfaces by introducing two related discrete-time dynamical systems. First, we discuss the Rauzy-Veech induction, highlighting its connections to interval…
For a compact three-dimensional smooth Riemannian manifold of strictly 1/4-pinched negative sectional curvature, we establish exponential mixing of the frame flow with respect to the normalized volume. More generally this result extends to…