Related papers: Infinitely many Riemann surfaces with transitive a…

We show that there is an infinite group of special automorphisms of the deformed group of diffeomorphisms, which describes parallel transports in Riemannian spaces of any variable curvature. Generators of translations of such group contain…

We show that a non-wandering endomorphism of the torus with invertible linear part without invariant directions and for which the critical points are in some sense generic is transitive. This improves a result of Andersson by allowing…

We prove the existence of infinitely many periodic points of symplectomorphisms isotopic to the identity if they admit at least one (non-contractible) hyperbolic periodic orbit and satisfy some condition on its flux. The obtained periodic…

We extend the unpublished work of M. Handel and R. Miller on the classification, up to isotopy, of endperiodic automorphisms of surfaces. We give the Handel-Miller construction of the geodesic laminations, give an axiomatic theory for…

We give an explicit description of smoothly bounded Reinhardt domains with noncompact automorphism groups. In particular, this description confirms a special case of a conjecture of Greene/Krantz.

We prove a "gluing" theorem for monotone homotopies; a monotone homotopy is a homotopy through simple contractible closed curves which themselves are pairwise disjoint. We show that two monotone homotopies which have appropriate overlap can…

We study automorphisms of the Hilbert scheme of $n$ points on a generic projective K3 surface $S$, for any $n \geq 2$. We show that the automorphism group of $S^{[n]}$ is either trivial or generated by a non-symplectic involution and we…

Given two semistable, non potentially isotrivial elliptic surfaces over a curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the…

We prove the conjecture of Berest-Eshmatov-Eshmatov by showing that the group of automorphisms of a product of Calogero-Moser spaces $C_{n_i}$, where the $n_i$ are pairwise distinct, acts $m$-transitively for each $m$.

We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a…

We study when a continuous isometric action of a Polish group on a complete metric space is, or can be, transitive. Our main results consist of showing that certain Polish groups, namely $\mathrm{Aut}^*(\mu)$ and $\mathrm{Homeo}^+[0,1]$,…

We classify simple groups that act by birational transformations on compact complex K\"ahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective…

We study the hyperbolicity properties of the action of a non-elementary automorphism group on a compact complex surface, with an emphasis on K3 and Enriques surfaces. A first result is that when such a group contains parabolic elements,…

A digraph is $s$-arc-transitive if its automorphism group is transitive on directed paths with $s$ edges, that is, on $s$-arcs. Although infinite families of finite $s$-arc transitive digraphs of arbitrary valency were constructed by the…

We show that every open Riemann surface can be obtained by glueing together a countable collection of equilateral triangles, in such a way that every vertex belongs to finitely many triangles. Equivalently, it is a _Belyi surface_: There…

We prove that Ahlfors 2-regular quasisymmetric images of the Euclidean plane are bi-Lipschitz images of the plane if and only if they are uniformly bi-Lipschitz homogeneous with respect to a group. We also prove that certain geodesic spaces…

We show that Riemann surfaces, and separated variables immediately provide classical Poisson commuting Hamiltonians. We show that Baxter's equations for separated variables immediately provide quantum commuting Hamiltonians. The…

The present work completes the classification of the compact Riemann surfaces of genus g with an analytic automorphism of order p (prime number) and p > g. More precisely, we construct a parameteriza- tion space for them, we compute their…

We prove a Poincar\'e-Bendixson theorem describing the asymptotic behavior of geodesics for a meromorphic connection on a compact Riemann surface. We shall also briefly discuss the case of non-compact Riemann surfaces, and study in detail…

We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the…