The ACO Seminar (2012-2013)
, 3:30pm, Wean 8220
Efficient partitioning of Euclidean space and incidence
The polynomial partitioning theorem of Guth and Katz has led to many
new bounds on the number of incidences between points and various
types of geometric objects such as lines, planes, spheres, etc. The
general paradigm is as follows. Simple geometric considerations give
crude bounds on the number of incidences between points and various
types of geometric objects. These bounds can then be strengthened by
partitioning Euclidean space into disjoint "cells," applying the crude
bound within each cell, and then summing the resulting contributions.
I will discuss these techniques, some recent results, and some open
problems in this field.
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