Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...
We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that split ...
We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection–diffusion–reaction equations based on the COmpRessed SolvING (CORSING) paradigm. Combining the Petrov–Galerkin technique with the compressed ...
Essentially nonoscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely employed to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well s ...
We describe an injection from border-strip decompositions of certain diagrams to permutations. This allows us to provide enumeration results as well as q-analogues of enumeration formulas. Finally, we use this injection to prove a connection between the nu ...
Previous studies assessed cultural ecosystem services (CES) at the local scale but often ignored them in national assessments. This paper explores CES relationships in Switzerland using web-based participatory mapping. We identified the spatial relationshi ...
We consider the numerical approximation of geometric Partial Differential Equations (PDEs) defined on surfaces in the 3D space. In particular, we focus on the geometric PDEs deriving from the minimization of an energy functional by L2L2-gradient flow. We a ...
This thesis consists of two parts. The first part is about a variant of Banach's fixed point theorem and its applications to several partial differential equations (PDE's), abstractly of the form Lu+Q(u)=f. The main result of thi ...
We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitate ...
Hyperbolic partial differential equations (PDEs) are mathematical models of wave phenomena, with applications in a wide range of scientific and engineering fields such as electromagnetic radiation, geosciences, fluid and solid mechanics, aeroacoustics, and ...
In this paper we construct quasiconformal embeddings from Y-pieces that contain a short boundary geodesic into degenerate ones. These results are used in a companion paper to study the Jacobian tori of Riemann surfaces that contain small simple closed geod ...
We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent ...
This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the Riemannian metrics th ...
The goal of this document is to provide a generalmethod for the computational approach to the topology and geometry of compact Riemann surfaces. The approach is inspired by the paradigms of object oriented programming. Our methods allow us in particular to ...
We study Sobolev-type metrics of fractional order s a parts per thousand yen 0 on the group Diff (c) (M) of compactly supported diffeomorphisms of a manifold M. We show that for the important special case M = S (1), the geodesic distance on Diff (c) (S (1) ...
The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...
Consider a diffusion field induced by a finite number of localized and instantaneous sources. In this paper, we study the problem of estimating these sources (including their intensities, spatial locations, and activation time) from the spatiotemporal samp ...
This paper introduces a subgradient descent algorithm to compute a Riemannian metric that minimizes an energy involving geodesic distances. The heart of the method is the Subgradient Marching Algorithm to compute the derivative of the geodesic distance wit ...
The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...
In recent work of Brock's, the pants graph is shown to be a combinatorial model for the completion of the Weil-Petersson metric on Teichmuller space. We prove that every Farey graph embedded in the pants graph is totally geodesic, in analogy with the extri ...
