AstonishingASsociate Team On NonISH euclIdeaN Geometry 
Principal investigators  
(Vegas, then)
Gamble common projectteam
INRIA Nancy  Grand Est, LORIA  Coordinator: Monique Teillaud 
Johann Bernouilli Institute of Mathematics and Computer Science
University of Groningen  Coordinator: Gert Vegter  
Other participating sites  
Mathematics Research Unit
University of Luxembourg  Coordinator: JeanMarc Schlenker 
Laboratoire d'Informatique Gaspard Monge
MarnelaVallée  Coordinator: Éric Colin de Verdière 
We aim at studying various structures and algorithms in other spaces than R^{d}, 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 longerterm integrations into CGAL, in order
to disseminate our results to endusers.
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.
2017  
September 2529 
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 2931 
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 1418 
Andrew Yarmola visits INRIA.
He gives a talk: "Hyperbolic 3manifolds 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. 