122 research outputs found
On the number of connected components of the ramification locus of a morphism of Berkovich curves
Let be a complete, nontrivially valued non-archimedean field. Given a
finite morphism of quasi-smooth -analytic curves that admit finite
triangulations, we provide upper bounds for the number of connected components
of the ramification locus in terms of topological invariants of the source
curve such as its topological genus, the number of points in the boundary and
the number of open ends.Comment: 20 pages, 3 figures; Final version, Accepted in Mathematische Annale
Density of automorphic points in deformation rings of polarized global Galois representations
Conjecturally, the Galois representations that are attached to essentially
selfdual regular algebraic cuspidal automorphic representations are
Zariski-dense in a polarized Galois deformation ring. We prove new results in
this direction in the context of automorphic forms on definite unitary groups
over totally real fields. This generalizes the infinite fern argument of
Gouvea-Mazur and Chenevier, and relies on the construction of non-classical
-adic automorphic forms, and the computation of the tangent space of the
space of trianguline Galois representations. This boils down to a surprising
statement about the linear envelope of intersections of Borel subalgebras
A Level Set Approach for Denoising and Adaptively Smoothing Complex Geometry Stereolithography Files
abstract: Stereolithography files (STL) are widely used in diverse fields as a means of describing complex geometries through surface triangulations. The resulting stereolithography output is a result of either experimental measurements, or computer-aided design. Often times stereolithography outputs from experimental means are prone to noise, surface irregularities and holes in an otherwise closed surface.
A general method for denoising and adaptively smoothing these dirty stereolithography files is proposed. Unlike existing means, this approach aims to smoothen the dirty surface representation by utilizing the well established levelset method. The level of smoothing and denoising can be set depending on a per-requirement basis by means of input parameters. Once the surface representation is smoothened as desired, it can be extracted as a standard levelset scalar isosurface.
The approach presented in this thesis is also coupled to a fully unstructured Cartesian mesh generation library with built-in localized adaptive mesh refinement (AMR) capabilities, thereby ensuring lower computational cost while also providing sufficient resolution. Future work will focus on implementing tetrahedral cuts to the base hexahedral mesh structure in order to extract a fully unstructured hexahedra-dominant mesh describing the STL geometry, which can be used for fluid flow simulations.Dissertation/ThesisMasters Thesis Aerospace Engineering 201
AlSub: Fully Parallel and Modular Subdivision
In recent years, mesh subdivision---the process of forging smooth free-form
surfaces from coarse polygonal meshes---has become an indispensable production
instrument. Although subdivision performance is crucial during simulation,
animation and rendering, state-of-the-art approaches still rely on serial
implementations for complex parts of the subdivision process. Therefore, they
often fail to harness the power of modern parallel devices, like the graphics
processing unit (GPU), for large parts of the algorithm and must resort to
time-consuming serial preprocessing. In this paper, we show that a complete
parallelization of the subdivision process for modern architectures is
possible. Building on sparse matrix linear algebra, we show how to structure
the complete subdivision process into a sequence of algebra operations. By
restructuring and grouping these operations, we adapt the process for different
use cases, such as regular subdivision of dynamic meshes, uniform subdivision
for immutable topology, and feature-adaptive subdivision for efficient
rendering of animated models. As the same machinery is used for all use cases,
identical subdivision results are achieved in all parts of the production
pipeline. As a second contribution, we show how these linear algebra
formulations can effectively be translated into efficient GPU kernels. Applying
our strategies to , Loop and Catmull-Clark subdivision shows
significant speedups of our approach compared to state-of-the-art solutions,
while we completely avoid serial preprocessing.Comment: Changed structure Added content Improved description
Multivariate Splines and Algebraic Geometry
Multivariate splines are effective tools in numerical analysis and approximation theory. Despite an extensive literature on the subject, there remain open questions in finding their dimension, constructing local bases, and determining their approximation power. Much of what is currently known was developed by numerical analysts, using classical methods, in particular the so-called Bernstein-B´ezier techniques. Due to their many interesting structural properties, splines have become of keen interest to researchers in commutative and homological algebra and algebraic geometry. Unfortunately, these communities have not collaborated much. The purpose of the half-size workshop is to intensify the interaction between the different groups by bringing them together. This could lead to essential breakthroughs on several of the above problems
Smoothness and Classicality on eigenvarieties
Let p be a prime number and f an overconvergent p-adic automorphic form on a
definite unitary group which is split at p. Assume that f is of "classical
weight" and that its Galois representation is crystalline at places dividing p,
then f is conjectured to be a classical automorphic form. We prove new cases of
this conjecture in arbitrary dimension by making crucial use of the "patched
eigenvariety"
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