Objective We consider problems in geometric and probabilistic combinatorics and discuss some applications to and connections with other areas.One underlying theme of our proposal is discrete isoperimetric relations.On the probabilistic side we discuss applications of Fourier analysis of Boolean functions to the study of threshold behavior of random graphs and other stochastic models, and propose ten directions for this emerging theory. One crucial problem is the study of near equality cases of Harper's isoperimetric inequality.On the geometric side we discuss the relation between the number of (k-1)-dimensional faces and the number of k-dimensional faces for complexes that can be embedded in 2k-dimensions. We also consider metrical and algorithmical problems on graphs of polytopes and Helly-type theorems. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisfourier analysisnatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics 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-2012-ADG_20120216 See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Host institution THE HEBREW UNIVERSITY OF JERUSALEM EU contribution € 1 376 504,00 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Israel See on map Activity type Higher or Secondary Education Establishments Principal investigator Gil Kalai (Prof.) Administrative Contact Hani Ben-Yehuda (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all THE HEBREW UNIVERSITY OF JERUSALEM Israel EU contribution € 1 376 504,00 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem See on map Activity type Higher or Secondary Education Establishments Principal investigator Gil Kalai (Prof.) Administrative Contact Hani Ben-Yehuda (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data