Cutting Circles into Pseudo-segments and Improved Bounds for Incidences [.ps]
An Improved Bound for k-sets in Three Dimensions [.ps]
Arrangements of curves and surfaces have been a major topic of study in computational and combinatorial geometry for more than 15 years. The field has progressed from analysis of two-dimensional arrangements in the 80's and early 90's to analysis of arrangements in three and higher dimensions. The progress included sharp bounds on the complexity of lower envelopes, single cells, zones, vertical decompositions, as well as finding many applications of these bounds to diverse areas, such as motion planning and geometric optimization. In the past couple of years more progress has been made on various major problems in the combinatorics of arrangements, and the purpose of this talk is to survey some of this progress. The main topics that I will survey are: