Related papers: An analytic approach to $P$-adic diffeomorphism gr…

Besides the oscillator group, there is another four-dimensional non-abelian solvable Lie group that admits a bi-invariant pseudo-Riemannian metric. It is called split oscillator group (sometimes also hyperbolic oscillator group or Boidol's…

This is a mathematical commentary on Teichm{\"u}ller's paper ``Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Fl{\"a}chen'' (Determination of extremal quasiconformal maps of closed oriented…

In this work we will show that the Teichm\"{u}ller distance for all elements of a certain class of generalized polynomial-like maps (the class of off-critically hyperbolic generalized polynomial-like maps) is actually a distance, as in the…

We consider Thompson's groups from the perspective of mapping class groups of surfaces of infinite type. This point of view leads us to the braided Thompson groups, which are extensions of Thompson's groups by infinite (spherical) braid…

We give an exposition of the theory of invariant manifolds around a fixed point, in the case of time-discrete, analytic dynamical systems over a complete ultrametric field K. Typically, we consider an analytic manifold M modelled on an…

This paper is a continuation of a previous paper in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper…

We present a nonstandard hull construction for locally uniform groups in a spirit similar to Luxembourg's construction of the nonstandard hull of a uniform space. Our nonstandard hull is a local group rather than a global group. We…

We compute the group of Morita self-equivalences (the Picard group) of a Poisson structure on an orientable surface, under the assumption that the degeneracies of the Poisson tensor are linear. The answer involves mapping class groups of…

Motivated by the interesting and yet scattered developments in representation theory of Banach-Lie groups, we discuss several functional analytic issues which should underlie the notion of infinite-dimensional reductive Lie group: norm…

We call a unital locally convex algebra $A$ a continuous inverse algebra if its unit group $A^\times$ is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group $G$ on a…

In this short note, we show that a natural generalization of the $p$-adic Fourier theory of Schneider and Teitelbaum follows immediately from the classification of $p$-divisible groups over $\cal{O}_{\mathbb{C}_p}$ by Scholze and Weinstein.…

There is a completely natural and intimate relationship between the diffeomorphism group of the circle and the Teichm\"uller spaces of Riemann surfaces discovered by us in 1988. Such a relationship had been sought-after by physicists from…

A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of…

Arnold showed that the Euler equations of an ideal fluid describe geodesics on the Lie algebra of incompressible vector fields. We generalize this to fluids with dissipation and Gaussian random forcing. The dynamics is determined by the…

In the proof of Crew's parabolicity conjecture, we established a key property concerning the slopes of $\dagger$-hulls of $F$-isocrystals, extending a result of Tsuzuki. This article presents an alternative proof of this theorem for a…

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichm\"uller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

Let $p$ be a prime number. Let $X/E$ be a geometrically connected, smooth, quasi-projective variety over a finite extension $E/\mathbb{Q}_p$. In this paper I demonstrate the existence of isomorphs of the tempered (and hence also \'etale)…

By Grothendieck's anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number-fields encode all the arithmetic…

A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in C.R. Acad. Sci. Paris s\'er. {\bf I 333} (2001) 763-768. We study…

Following Robert's [26], we study the structure of unitary groups and groups of approximately inner automorphisms of unital $C^*$-algebras, taking advantage of the former being Banach-Lie groups. For a given unital $C^*$-algebra $A$, we…