Obiettivo
The central goal of this proposal is to settle the algorithmic
foundations of geometry understanding in dimensions higher than 3. We
coin the term geometry understanding to encompass a collection
of tasks including the computer representation and the approximation
of geometric structures, and the inference of geometric or topological
properties of sampled shapes.
The need to understand geometric structures is ubiquitous in science
and has become an essential part of scientific computing and
data analysis.
Geometry understanding is by no means limited to
three dimensions. Many applications in physics, biology,
and
engineering require a keen understanding of the geometry of a variety
of higher dimensional spaces to
capture concise information from the underlying often highly
nonlinear structure of
data. Our approach is complementary to manifold learning
techniques and aims at developing an effective theory for geometric and
topological data analysis.
To reach these objectives, the guiding principle will be to foster a
symbiotic relationship between theory and practice, and to address
fundamental research issues along three parallel advancing
fronts. We will simultaneously develop mathematical approaches
providing theoretical guarantees, effective algorithms that are
amenable to theoretical analysis and rigorous experimental validation,
and perennial software development. We will undertake the
development of a high-quality open source software platform to
implement the most important geometric data structures and algorithms
at the heart of geometry understanding in higher dimensions. The
platform will be a unique vehicle towards researchers from other
fields and will serve as a basis for groundbreaking advances in
scientific computing and data analysis.
Campo scientifico
Invito a presentare proposte
ERC-2013-ADG
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Meccanismo di finanziamento
ERC-AG - ERC Advanced GrantIstituzione ospitante
78153 Le Chesnay Cedex
Francia