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11/23/2022
Improved Elekes-Szabó type estimates using proximity
We prove a new Elekes-Szabó type estimate on the size of the intersectio...
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12/08/2020
On rich lenses in planar arrangements of circles and related problems
We show that the maximum number of pairwise non-overlapping k-rich lense...
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06/16/2020
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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02/26/2020
Sphere tangencies, line incidences, and Lie's line-sphere correspondence
Two spheres with centers p and q and signed radii r and s are said to be...
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04/21/2019
Constructive Polynomial Partitioning for Algebraic Curves in R^3 with Applications
In 2015, Guth proved that for any set of k-dimensional varieties in R^d ...
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12/26/2018
An Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications
Guth showed that given a family S of n g-dimensional semi-algebraic sets...
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07/17/2018
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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06/16/2017