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Qualifying Exam
4/11/2016 11:00 am
Hill 482

A refined energy bound for distinct perpendicular bisectors

Benjamin Lund, Rutgers University

Examination Committee: Shubhangi Saraf (advisor), Swastik Kopparty, Mario Szegedy and Santosh Nagarakatte

Abstract

Many problems in discrete geometry and additive combinatorics ask for the fewest distinct equivalence classes that may be determined by a set of n points or numbers under some algebraically defined equivalence relation. For example, Erdős asked for the fewest distinct distances determined by any set of n points in the Euclidean plane.

I will give a brief survey of some classic and recent results on questions of this sort. I will then discuss a recent result on the fewest distinct perpendicular bisectors determined by any set of n points in the plane.