Related papers: A compactness theorem for frozen planets
We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.
We characterize the compactness properties of the product of \lambda\ copies of the space \omega\ with the discrete topology, dealing in particular with the case \lambda\ singular, using regular and uniform ultrafilters, infinitary…
We consider moduli fields interacting with thermalized relativistic matter. We determine the temperature dependence of their damping rate and find it is dominated by thermal effects in the high temperature regime, i.e. for temperatures…
We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the…
We construct a new compactification of the moduli space H_g of smooth hyperelliptic curves of genus g. We compare our compactification with other well-known remarkable compactifications of H_g .
The period is a classical complex analytic invariant for a compact Riemann surface defined by integration of differential 1-forms. It has a strong relationship with the complex structure of the surface. In this chapter, we review another…
Volume of moduli space of BPS vortices on a compact genus h Riemann surface Sigma_h is evaluated by means of topological field theory and localization technique. Vortex in Abelian gauge theory with a single charged scalar field (ANO vortex)…
We prove that the orbits of a polar action of a compact Lie group on a compact rank one symmetric space are tautly embedded with respect to Z_2-coefficients.
Premelting describes the confluence of phenomena that are responsible for the stable existence of the liquid phase of matter in the solid region of its bulk phase diagram. Here we develop a theoretical description of the premelting of water…
In this paper we consider the moduli space of complete, conformally flat metrics on a sphere with k punctures having constant positive Q-curvature and positive scalar curvature. Previous work has shown that such metrics admit an asymptotic…
The primary goal of this paper is to find a homotopy theoretic approximation to moduli spaces of holomorphic maps Riemann surfaces into complex projective space. There is a similar treatment of a partial compactification of these moduli…
Equilibrium properties of hydrogen-helium mixtures under thermodynamic conditions found in the interior of giant gas planets are studied by means of density functional theory molecular dynamics simulations. Special emphasis is placed on the…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
We have found an isolated polar disk galaxy in what appears to be a cosmological wall situated between two voids. This void galaxy is unique as its polar disk was discovered serendipitously in an HI survey of SDSS void galaxies, with no…
The aim of the note is to extend the uniformization theorem to compact Kahler spaces X with mild singularities and establish a kind of rigidity of their universal coverings. We assume the fundamental group of X is large, residually finite…
We classify polar isometric actions on simply connected 3-dimensional Riemannian homogeneous spaces, up to orbit equivalence. In particular, we classify extrinsically homogeneous surfaces in such spaces and study the geometry of the orbit…
In this review chapter we focus on the many-body dynamics of cold polar molecules in the strongly interacting regime. In particular, we discuss a toolbox for engineering many-body Hamiltonians based on the manipulation of the electric…
A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable…
Melting of two dimensional (2D) clusters of classical particles is studied using Brownian dynamics and Langevin molecular dynamics simulations. The particles are confined by a circular hard wall or a parabolic external potential and…
Besides being a source of energy, light can also cool gases of atoms down to the lowest temperatures ever measured, where atomic motion almost stops. The research field of cold atoms has emerged as a multidisciplinary one, highly relevant,…