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Canonical tessellations of decorated hyperbolic surfaces
A decoration of a hyperbolic surface of finite type is a choice of circle, horocycle or hypercycle about each cone-point, cusp or flare of the...
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Adaptive and Frugal FETI-DP for Virtual Elements
The FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) method has recently successfully been applied to virtual element...
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Generating Star-Shaped Blocks for Scaled Boundary Multipatch IGA
This paper deals with the decomposition of a domain into star-shaped blocks, which is motivated by the idea of solving PDEs by means of the scaled...
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Radius Functions on Poisson–Delaunay Mosaics and Related Complexes Experimentally
Discrete Morse theory has recently lead to new developments in the theory of random geometric complexes. This article surveys the methods and results...
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Uniform convolution estimates for complex polynomial curves in \({\mathbb {C}}^3\)
We establish optimal ( p , q ) ranges for the weighted convolution operator associated with a complex polynomial curve. Establishing this estimate comes...
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Random colorings in manifolds
We develop a general method for constructing random manifolds and sub-manifolds in arbitrary dimensions. The method is based on associating colors to...
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Spectral Methods for Gaussian Processes
The quantization theory of Gaussian random vectors in a Hilbert space is ruled by the eigenvalues and eigenvectors of their covariance operators....
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Optimal Transport for Generative Models
Optimal transport plays a fundamental role in deep learning. Natural data sets have intrinsic patterns, which can be summarized as the manifold...
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Monotone Discretization of Anisotropic Differential Operators Using Voronoi’s First Reduction
We consider monotone discretization schemes, using adaptive finite differences on Cartesian grids, of partial differential operators depending on a...
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Kuga Fiber Spaces
This chapter is in a sense the culmination of the various topics discussed in previous chapters; it arises by the restriction of the considered...
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Universal Karyon Tilings
Universal karyon tilings 𝒯 d ( v , μ ) of the real d-dimensional space ℝ d are constructed. These tilings depend on two free parameters: the star v = { v 0 ,...
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Curvature Sets Over Persistence Diagrams
We study a family of invariants of compact metric spaces that combines the Curvature Sets defined by Gromov in the 1980 s with Vietoris–Rips...
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Gromov’s Waist of Non-radial Gaussian Measures and Radial Non-Gaussian Measures
We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean space, motivated by the famous theorem of Gromov about the...
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Optimal Transport for Generative Models
Optimal transport plays a fundamental role in deep learning. Natural data sets have intrinsic patterns, which can be summarized as the manifold...
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The continuous stochastic gradient method: part II–application and numerics
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology...
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Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant...
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Local formulas for Ehrhart coefficients from lattice tiles
As shown by McMullen in 1983, the coefficients of the Ehrhart polynomial of a lattice polytope can be written as a weighted sum of facial volumes....
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Complements in Functional Analysis
Functional analysis deals with properties of spaces of functions (or of sequences), rather than of individual objects. To study a specific function...