New Trends in Intuitive Geometry

Gergely Ambrus is a researcher at the Alfréd Rényi Institute of Mathematics, working in discrete, convex and stochastic geometry and discrete analysis. He has organized several conferences in the field. Imre Bárány is a research professor at the Alfréd Rényi Institute of Mathematics in Budapest and the Astor Professor of Mathematics at University College London. His main field of interest is discrete and convex geometry, and random points and lattice points in convex bodies, with applications in computer science, operations research, and elsewhere. He was an invited speaker at ICM 2002, Beijing. He has organized several conferences in discrete and convex geometry including three in Oberwolfach on Discrete Geometry.

Introduction.- A. Barvinok: The tensorization trick in geometry.- K. Bezdek and M. A. Khan: Contact numbers for sphere packings.- P. M. Blagojevic, A. S. D. Blagojevic, and G. M. Ziegler: The topological Tverberg theorem plus constraints.- B. Csikós: On the volume of Boolean expressions of balls - A review of the Kneser-Poulsen conjecture.- F. de Zeeuw: A survey of Elekes-Rónyai-type problems.- G. Domokos and G. W. Gibbons: The geometry of abrasion.- F. M. de Oliveira Filho and F. Vallentin: Computing upper bounds for the packing density of congruent copies of a convex body.- P. Hajnal and E. Szemerédi: Two geometrical applications of the semi-random method.- A. F. Holmsen: Erdös-Szekeres theorems for families of convex sets.- R. Kusner, W. Kusner, J. C. Lagarias, and S. Shlosman: Configuration spaces of equal spheres touching a given sphere: the twelve spheres problem.- E. León and G. M. Ziegler: Spaces of convex n-partitions.- P. McMullen: New regular compounds of 4-polytopes.- O.R. Musin, Five Essays on the Geometry of László Fejes Tóth.- M. Naszódi: Flavors of translative coverings.- M. Sharir and Noam Solomon: Incidences between points and lines in three dimensions.- J. Solymosi and F. de Zeeuw: Incidence bounds for complex algebraic curves on Cartesian products.- K. J. Swanepoel: Combinatorial distance geometry in normed spaces.