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Algorithms, Combinatorics and Optimization Seminar
For more information, please visit the home page for the program in Algorithms, Combinatorics and Optimization at Carnegie Mellon University.
Carnegie Mellon University offers an interdisciplinary Ph.D program in Algorithms, Combinatorics and Optimization. This program is the first of its kind in the United States. It is administered jointly by the Tepper School of Business (Operations Research group), the Computer Science Department (Algorithms and Complexity group) and the Department of Mathematical Sciences (Discrete Mathematics group). (Learn more...)
Title: Efficient partitioning of Euclidean space and incidence theorems
Abstract: 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.
Date: Thursday, October 11, 2012
Time: 3:30 pm
Location: Wean 8220
Submitted by: Loh