Objective Title: Discrete and convex geometry: challenges, methods, applicationsAbstract: Research in discrete and convex geometry, using tools from combinatorics, algebraictopology, probability theory, number theory, and algebra, with applications in theoreticalcomputer science, integer programming, and operations research. Algorithmic aspects areemphasized and often serve as motivation or simply dictate the questions. The proposedproblems can be grouped into three main areas: (1) Geometric transversal, selection, andincidence problems, including algorithmic complexity of Tverberg's theorem, weakepsilon-nets, the k-set problem, and algebraic approaches to the Erdos unit distance problem.(2) Topological methods and questions, in particular topological Tverberg-type theorems,algorithmic complexity of the existence of equivariant maps, mass partition problems, and thegeneralized HeX lemma for the k-coloured d-dimensional grid. (3) Lattice polytopes and randompolytopes, including Arnold's question on the number of convex lattice polytopes, limitshapes of lattice polytopes in dimension 3 and higher, comparison of random polytopes andlattice polytopes, the integer convex hull and its randomized version. Fields of science natural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicsapplied mathematicsstatistics and probability 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-2010-AdG_20100224 See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Coordinator RENYI ALFRED MATEMATIKAI KUTATOINTEZET Address Realtanoda street 13-15 1053 Budapest Hungary See on map Region Közép-Magyarország Budapest Budapest Activity type Other Principal investigator Imre Barany (Dr.) Administrative Contact Tiziana Del Viscio (Ms.) Links Contact the organisation Opens in new window Website Opens in new window EU contribution No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all RENYI ALFRED MATEMATIKAI KUTATOINTEZET Hungary EU contribution € 1 298 012,28 Address Realtanoda street 13-15 1053 Budapest See on map Region Közép-Magyarország Budapest Budapest Activity type Other Principal investigator Imre Barany (Dr.) Administrative Contact Tiziana Del Viscio (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Other funding No data
