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." Fields of science natural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsnumerical analysisnatural sciencesphysical sciencestheoretical physics Programme(s) 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) Topic(s) ERC-AG-PE1 - ERC Advanced Grant - Mathematical foundations Call for proposal ERC-2009-AdG See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Coordinator FREIE UNIVERSITAET BERLIN Address Kaiserswerther strasse 16-18 14195 Berlin Germany See on map Region Berlin Berlin Berlin Activity type Higher or Secondary Education Establishments Principal investigator Günter Matthias Ziegler (Prof.) Administrative Contact Sindy Kretschmer (Ms.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution € 1 726 385,25 Beneficiaries (2) Sort alphabetically Sort by EU Contribution Expand all Collapse all FREIE UNIVERSITAET BERLIN Germany EU contribution € 1 726 385,25 Address Kaiserswerther strasse 16-18 14195 Berlin See on map Region Berlin Berlin Berlin Activity type Higher or Secondary Education Establishments Principal investigator Günter Matthias Ziegler (Prof.) Administrative Contact Sindy Kretschmer (Ms.) Links Contact the organisation Opens in new window Website Opens in new window TECHNISCHE UNIVERSITAT BERLIN Participation ended Germany EU contribution € 128 014,75 Address Strasse des 17 juni 135 10623 Berlin See on map Region Berlin Berlin Berlin Activity type Higher or Secondary Education Establishments Administrative Contact Silke Hönert (Ms.) Links Contact the organisation Opens in new window Website Opens in new window
