JournalsowrVol. 6 / No. 4DOI 10.4171/owr/2009/53

Convex Geometry and its Applications

  • Martin Henk

    Technische Universität Berlin, Germany
  • Keith M. Ball

    University of Warwick, Coventry, United Kingdom
  • Monika Ludwig

    Technische Universität Wien, Austria
Convex Geometry and its Applications cover

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Abstract

The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry, both the discrete and convex branches of it, has experienced a striking series of developments in the past 10 years. Several examples were presented at this meeting, for example the work of Rudelson et al. on conjunction matrices and their relation to confidential data analysis, that of Litvak et al. on remote sensing and a series of results by Nazarov and Ryabogin et al. on Mahler’s conjecture for the volume product of domains and their polars.