
On rich lenses in planar arrangements of circles and related problems
We show that the maximum number of pairwise nonoverlapping krich lense...
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Distinct distances in the complex plane
We prove that if P is a set of n points in ℂ^2, then either the points i...
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Sphere tangencies, line incidences, and Lie's linesphere correspondence
Two spheres with centers p and q and signed radii r and s are said to be...
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Constructive Polynomial Partitioning for Algebraic Curves in R^3 with Applications
In 2015, Guth proved that for any set of kdimensional varieties in R^d ...
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An Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications
Guth showed that given a family S of n gdimensional semialgebraic sets...
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Counting higher order tangencies for plane curves
We prove that n plane algebraic curves determine O(n^(k+2)/(k+1)) points...
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Breaking the 3/2 barrier for unit distances in three dimensions
We prove that every set of n points in R^3 spans O(n^295/197+ϵ) unit dis...
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Joshua Zahl
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