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Discrete Riemann Surfaces and the Ising Model
Abstract: We define a new theory of discrete Riemann surfaces and present its basic results. The key idea is to consider not only a cellular decomposition of a surface, but the union with its dual.Expand
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Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green’s function
Abstract Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. TheExpand
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Les entrelacs des enluminures celtes
A partir de graphes, vous pouvez creer de superbes entrelacs, a la maniere des enluminures celtes. Munissez vous de crayons et d'une gomme...
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Discrete Riemann Surfaces
We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincare dual, equipped with a discrete conformal structure. A lot ofExpand
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Integrable lattice realizations of conformal twisted boundary conditions
We construct integrable lattice realizations of conformal twisted boundary conditions for s�( 2) unitary minimal models on a torus. These conformal field theories are realized as the continuumExpand
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Holomorphie discrète et modèle d'Ising
Ma these generalise la notion de criticite pour le modele d'Ising en dimension 2. J'y definis une nouvelle notion d'holomorphie discrete sur une decomposition cellulaire d'une surface de Riemann. LeExpand
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Discrete period matrices and related topics
  • C. Mercat
  • Mathematics, Physics
  • 22 November 2001
We continue our investigation of Discrete Riemann Surfaces with the discussion of the discrete analogs of period matrices, Riemann's bilinear relations, exponential of constant argument, series andExpand
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Cross-Curriculum Search for Intergeo
TLDR
This paper describes the current prototypes, the input-methods, the workflows used, and the integration into the Intergeo platform. Expand
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Discrete Complex Structure on Surfel Surfaces
  • C. Mercat
  • Mathematics, Computer Science
  • DGCI
  • 12 February 2008
TLDR
This paper defines a theory of conformal parametrization of digital surfaces made of surfels equipped with a normal vector. Expand
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INTEROPERABLE INTERACTIVE GEOMETRY FOR EUROPE - FIRST TECHNOLOGICAL AND EDUCATIONAL RESULTS AND FUTURE CHALLENGES OF THE INTERGEO PROJECT
In this overview article we describe the manifold achievements and challenges of Intergeo, a project co-funded within the eContentplus programme of the European Union.
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