Objective The objective of this research proposal is to develop new methods to answer a number of fundamental questions generated by the recent development of modern analysis. The questions we are interested in are specifically related to the study of local structure of sets and functions in the classical Euclidean setting, in infinite dimensional Banach spaces and in the modern setting of analysis on metric spaces. The main areas of study will be:(a) Structure of null sets and representation of (singular) measures, one of the key motivations being the differentiability of Lipschitz functions in finite dimensional spaces.(b) Nonlinear geometric functional analysis, with particular attention to the differentiability of Lipschitz functions in infinite dimensional Hilbert spaces and Banach spaces with separable dual.(c) Foundations of analysis on metric spaces, the key problems here being representation results for Lipschitz differentiability spaces and spaces satisfying the Poincar\'e inequality.(d) Uniqueness of tangent structure in various settings, where the ultimate goal is to contribute to the fundamental problem whether minimal surfaces (in their geometric measure theoretic model as area minimizing integral currents) have a unique behaviour close to any point. Fields of science natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysis 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-2011-ADG_20110209 See other projects for this call Funding Scheme ERC-AG - ERC Advanced Grant Coordinator THE UNIVERSITY OF WARWICK Address Kirby corner road - university house CV4 8UW Coventry United Kingdom See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Administrative Contact Peter Hedges (Dr.) Principal investigator David Preiss (Prof.) 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 THE UNIVERSITY OF WARWICK United Kingdom EU contribution € 2 068 147,00 Address Kirby corner road - university house CV4 8UW Coventry See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Administrative Contact Peter Hedges (Dr.) Principal investigator David Preiss (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Other funding No data
