Cel The central goal of this proposal is to settle the algorithmicfoundations of geometry understanding in dimensions higher than 3. Wecoin the term geometry understanding to encompass a collectionof tasks including the computer representation and the approximationof geometric structures, and the inference of geometric or topologicalproperties of sampled shapes.The need to understand geometric structures is ubiquitous in scienceand has become an essential part of scientific computing anddata analysis.Geometry understanding is by no means limited tothree dimensions. Many applications in physics, biology,andengineering require a keen understanding of the geometry of a varietyof higher dimensional spaces tocapture concise information from the underlying often highlynonlinear structure ofdata. Our approach is complementary to manifold learningtechniques and aims at developing an effective theory for geometric andtopological data analysis.To reach these objectives, the guiding principle will be to foster asymbiotic relationship between theory and practice, and to addressfundamental research issues along three parallel advancingfronts. We will simultaneously develop mathematical approachesproviding theoretical guarantees, effective algorithms that areamenable to theoretical analysis and rigorous experimental validation,and perennial software development. We will undertake thedevelopment of a high-quality open source software platform toimplement the most important geometric data structures and algorithmsat the heart of geometry understanding in higher dimensions. Theplatform will be a unique vehicle towards researchers from otherfields and will serve as a basis for groundbreaking advances inscientific computing and data analysis. Dziedzina nauki nauki przyrodniczeinformatykanauka o danychnauki przyrodniczeinformatykaoprogramowanietworzenie oprogramowanianauki przyrodniczeinformatykanauki obliczeniowenauki przyrodniczematematykamatematyka czystageometria Program(-y) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Temat(-y) ERC-AG-PE6 - ERC Advanced Grant - Computer science and informatics Zaproszenie do składania wniosków ERC-2013-ADG Zobacz inne projekty w ramach tego zaproszenia System finansowania ERC-AG - ERC Advanced Grant Koordynator INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE Adres Domaine de voluceau rocquencourt 78153 Le chesnay cedex Francja Zobacz na mapie Region Ile-de-France Ile-de-France Yvelines Rodzaj działalności Research Organisations Kontakt administracyjny Marie Schiaffino (Mrs.) Kierownik naukowy Jean-Daniel Boissonnat (Dr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Wkład UE Brak danych Beneficjenci (1) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE Francja Wkład UE € 2 497 597,00 Adres Domaine de voluceau rocquencourt 78153 Le chesnay cedex Zobacz na mapie Region Ile-de-France Ile-de-France Yvelines Rodzaj działalności Research Organisations Kontakt administracyjny Marie Schiaffino (Mrs.) Kierownik naukowy Jean-Daniel Boissonnat (Dr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Środki z innych źródeł Brak danych