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Structured Discrete Models as a basis for studies in Geometry, Numerical Analysis, Topology, and Visualization

Objective

"Discrete structures appear throughout mathematics not only as approximations to continuous objects, but also as mathematical objects of their own right. The ""right"" discrete models should have analogous theory to the continuous limit, but often more transparent, more interesting structure, it ""tells you more"". The proposed project has the agenda to connect, and make substantial progress in, a number of interesting, but rather diverse instances for this, including
- Convex Polytopes as models for linear, semi-definite and non-linear optimization problems,
- Polyhedral Surfaces as models for differential geometry, including questions of (discrete) integrability,
- Structured meshes as the ""right"" discrete structures for solving systems of partial differential equations with quality guarantees,
- Triangulation models as they appear as models for space in quantum gravity.
In this simultaneous treatment of these topics we hope to capture connections and identify analogous and parallel structures in different parts of mathematics. This is a theory proposal, but a number of the core topics are suggested by applied research, as done e.g. in the framework of the Berlin DFG Research Center MATHEON in Berlin. It will connect to, and rely on, other major structured research groups in Berlin, such as the ""Polyhedral Surfaces"" DFG Research Group, and the Research Training Group led by the PI. In collaboration between individuals and groups with diverse mathematical expertise in Berlin, throughout Europe and beyond we are set to establish an additional ""theory backbone""; for applied research in Berlin."

Field of science

  • /natural sciences/mathematics/applied mathematics/numerical analysis
  • /natural sciences/mathematics/pure mathematics/topology
  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/mathematics
  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations

Call for proposal

ERC-2009-AdG
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant

Host institution

FREIE UNIVERSITAET BERLIN
Address
Kaiserswerther Strasse 16-18
14195 Berlin
Germany
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 726 385,25
Principal investigator
Günter Matthias Ziegler (Prof.)
Administrative Contact
Sindy Kretschmer (Ms.)

Beneficiaries (2)

FREIE UNIVERSITAET BERLIN
Germany
EU contribution
€ 1 726 385,25
Address
Kaiserswerther Strasse 16-18
14195 Berlin
Activity type
Higher or Secondary Education Establishments
Principal investigator
Günter Matthias Ziegler (Prof.)
Administrative Contact
Sindy Kretschmer (Ms.)
TECHNISCHE UNIVERSITAT BERLIN

Participation ended

Germany
EU contribution
€ 128 014,75
Address
Strasse Des 17 Juni 135
10623 Berlin
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Silke Hönert (Ms.)