Astonishing

ASsociate Team On Non-ISH euclIdeaN Geometry



Principal investigators
(Vegas, then) Gamble common project-team
INRIA Nancy -- Grand Est, LORIA
Coordinator: Monique Teillaud
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Johann Bernouilli Institute of Mathematics and Computer Science
University of Groningen
Coordinator: Gert Vegter
Other participating sites
Mathematics Research Unit
University of Luxembourg
Coordinator: Jean-Marc Schlenker
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Laboratoire d'Informatique Gaspard Monge
Marne-la-Vallée
Coordinator: Éric Colin de Verdière


[Scientific Objectives] - [Workshops] - [Visits] - [Publications]

Scientific Objectives

We aim at studying various structures and algorithms in other spaces than Rd, from a computational geometry viewpoint. Proposing algorithms operating in such spaces requires a prior deep study of the mathematical properties of the objects considered, which raises new fundamental and difficult questions that we want to tackle.

Methodology. A key characteristic of the project is its interdisciplinarity: it gathers approaches, knowledge, and tools in mathematics and computer science.
A mathematical study of the considered objects will be performed, together with the design of algorithms when applicable. Algorithms will be analyzed both in theory and in practice after prototype implementations. In the long term, implementations should be improved whenever it makes sense to target longer-term integrations into CGAL, in order to disseminate our results to end-users.

Challenges. The global difficulty of this project is intrinsic to the differences between the classical Euclidean spaces and the spaces that we consider (to spot only one concrete example: translations in the hyperbolic plane do not commute). This prevents known algorithms of computational geometry from naturally extending to other spaces. The mathematical difficulties are real and new ideas will be necessary. The challenge is to provide new mathematical foundations for computational geometry, in order to allow the emergence of algorithms that will be both efficient in theory and effective in practice.


Workshops


Visits

2017  
September 25-29 Matthijs Ebbens visits INRIA.
The visit is partially supported by the University of Groningen.
September 18 - October 6 Gert Vegter visits INRIA.
The visit is partially supported by the University of Groningen.
May 8 - 19 Monique Teillaud visits U. Groningen.
The visit is partially supported by the University of Groningen.
May 15 - 19 Iordan Iordanov visits U. Groningen.
The visit is partially supported by the University of Groningen.
March 29-31 Iordan Iordanov visits U. Luxembourg.
The visit is partially supported by the University of Luxembourg.
January 30 Astonishing is accepted as an INRIA Associate Team
 
2016 NEAT [Nancy Emerging] ASsociate Team supported by INRIA Nancy -- Grand Est
December 15 - 16 Monique Teillaud visits U. Luxembourg.
The visit is partially supported by the University of Luxembourg.
November 14-18 Andrew Yarmola visits INRIA.
He gives a talk: "Hyperbolic 3-manifolds with low cusp volume".
The visit is mostly supported by the University of Luxembourg.
October 27 - 28 Monique Teillaud visits U. Luxembourg.
The visit is partially supported by the University of Luxembourg.
September 19 - 30 Monique Teillaud visits U. Groningen.
September 19 - 23 Iordan Iordanov visits U. Groningen.
June 14 - 18 Monique Teillaud attends SoCG in Boston. She gives the talk on our accepted paper.
June 1st - 30 Iordan Iordanov visits U. Luxembourg.
The visit is partially supported by the University of Luxembourg.
Apr 18 - May 13 Gert Vegter visits INRIA.
The visit is supported by the University of Lorraine.
February 18 Monique Teillaud and Iordan Iordanov visit U. Luxembourg.
Monique Teillaud gives a talk: "CGAL, geometry made practical" at the seminar Computer Science meets Mathematics.
The visit is partially supported by University of Luxembourg.


Publications



Monique Teillaud
Last modified: Mon Jul 24 11:03:00 CEST 2017