We present an algorithmic framework for producing Delaunay triangulations of manifolds. The input to the algorithm is a set of sample points together with coordinate patches indexed by those points. The transition functions between nearby coordinate patches are required to be bi-Lipschitz with a constant close to 1. The primary novelty of the framework is that it can accommodate abstract manifo...

In this paper, we describe an example of a hyperkähler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can be furthermore identified either with the cotangent space of a connected component Gr res, (...

Informed by object-oriented and relational perspectives on space, this article argues for morecomplex accounts of architectural and urban problématiques. Starting from Isabelle Stengers’distinction between la ville complexe and la ville compliquée, it discusses the 2010 exhibition“Building for Brussels. Architecture and Urban Transformation in Europe” (BOZAR, Centre ofFine Arts ...

This is a survey of M-regularity and its applications, expanding on lectures given by the second author at the Seattle conference, in August 2005, and at the Luminy workshop " Géométrie Algébrique Complexe " , in October 2005 1 .

In this paper, we describe an example of a hyperkähler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can furthermore be identified either with the cotangent space of a connected component Gr res of...

A tropical curve Γ is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system |D| of a divisor D on a tropical curve Γ analogously to the classical counterpart. We investigate the structure of |D| as a cell complex and show that linear systems are quotients of tropical modul...

We show that the moduli space M of marked cubic surfaces is biholomorphic to (B −H)/Γ0 where B is complex hyperbolic four-space, where Γ0 is a specific group generated by complex reflections, and where H is the union of reflection hyperplanes for Γ0. Thus M has a complex hyperbolic structure, i.e., an (incomplete) metric of constant holomorphic sectional curvature. Une structure hyperbolique co...