Joshua Zahl

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All published works

Action	Title	Year	Authors
+ PDF Chat	Improved $L^p$ bounds for the strong spherical maximal operator	2025	Jonathan E. Hickman Joshua Zahl
+	On the Dimension of Exceptional Parameters for Nonlinear Projections, and the Discretized Elekes-Rónyai Theorem	2024	Orit E. Raz Joshua Zahl
+	The Assouad dimension of Kakeya sets in $\mathbb{R}^3$	2024	Hong Wang Joshua Zahl
+	Improved Elekes-Szabó type estimates using proximity	2023	József Solymosi Joshua Zahl
+ PDF Chat	A note on Fourier restriction and nested Polynomial Wolff axioms	2023	Jonathan Hickman Joshua Zahl
+ PDF Chat	Unions of lines in Rn$\mathbb {R}^n$	2023	Joshua Zahl
+	On Maximal Functions Associated to Families of Curves in the Plane	2023	Joshua Zahl
+ PDF Chat	Kakeya sets from lines in $SL_2$	2022	Nets Hawk Katz Shukun Wu Joshua Zahl
+	Counting and Cutting Rich Lenses in Arrangements of Circles	2022	Esther Ezra Orit E. Raz Micha Sharir Joshua Zahl
+	A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\mathbb{R}^3$	2022	Malabika Pramanik Tongou Yang Joshua Zahl
+	Unions of lines in $\mathbb{R}^n$	2022	Joshua Zahl
+	Sticky Kakeya sets and the sticky Kakeya conjecture	2022	Hong Wang Joshua Zahl
+	Kakeya sets from lines in $SL_2$	2022	Nets Hawk Katz Shukun Wu Joshua Zahl
+	Improved Elekes-Szabó type estimates using proximity	2022	József Solymosi Joshua Zahl
+	On rich lenses in planar arrangements of circles and related problems	2021	Esther Ezra Orit E. Raz Micha Sharir Joshua Zahl
+	Erratum: “Breaking the 3/2 barrier for unit distances in three dimensions”	2021	Micha Sharir Joshua Zahl
+ PDF Chat	Sphere tangencies, line incidences and Lie’s line-sphere correspondence	2021	Joshua Zahl
+	Distinct distances in the complex plane	2021	Adam Sheffer Joshua Zahl
+ PDF Chat	New Kakeya estimates using Gromov's algebraic lemma	2021	Joshua Zahl
+ PDF Chat	Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications	2021	Pankaj K. Agarwal Boris Aronov Esther Ezra Joshua Zahl
+	New estimates on the size of $(α,2α)$-Furstenberg sets	2021	Daniel Di Benedetto Joshua Zahl
+	On the dimension of exceptional parameters for nonlinear projections, and the discretized Elekes-Rónyai theorem	2021	Orit E. Raz Joshua Zahl
+ PDF Chat	Large Sets Avoiding Rough Patterns	2020	Jacob Denson Malabika Pramanik Joshua Zahl
+ PDF Chat	A Kakeya maximal function estimate in four dimensions using planebrushes	2020	Nets Hawk Katz Joshua Zahl
+	Distinct distances in the complex plane	2020	Adam Sheffer Joshua Zahl
+	Sphere tangencies, line incidences, and Lie's line-sphere correspondence	2020	Joshua Zahl
+	Dimension-expanding polynomials and the discretized Elekes-Rónyai theorem	2020	Orit E. Raz Joshua Zahl
+ PDF Chat	Constructive Polynomial Partitioning for Algebraic Curves in $\mathbb{R}^3$ with Applications	2020	Boris Aronov Esther Ezra Joshua Zahl
+	On rich lenses in planar arrangements of circles and related problems	2020	Esther Ezra Orit E. Raz Micha Sharir Joshua Zahl
+	A note on Fourier restriction and nested Polynomial Wolff axioms	2020	Jonathan E. Hickman Joshua Zahl
+	Distinct distances in the complex plane	2020	Adam Sheffer Joshua Zahl
+	Sphere tangencies, line incidences, and Lie's line-sphere correspondence	2020	Joshua Zahl
+ PDF Chat	On the Discretized Sum-Product Problem	2019	Larry Guth Nets Hawk Katz Joshua Zahl
+ PDF Chat	Counting higher order tangencies for plane curves	2019	Joshua Zahl
+	New Kakeya estimates using Gromov's algebraic lemma	2019	Joshua Zahl
+	Constructive Polynomial Partitioning for Algebraic Curves in $\mathbb{R}^3$ with Applications	2019	Boris Aronov Esther Ezra Joshua Zahl
+	A Kakeya maximal function estimate in four dimensions using planebrushes	2019	Nets Hawk Katz Joshua Zahl
+	New Kakeya estimates using Gromov's algebraic lemma	2019	Joshua Zahl
+	Constructive Polynomial Partitioning for Algebraic Curves in $\mathbb{R}^3$ with Applications	2019	Boris Aronov Esther Ezra Joshua Zahl
+	Large Sets Avoiding Rough Patterns	2019	Jacob Denson Malabika Pramanik Joshua Zahl
+	A Kakeya maximal function estimate in four dimensions using planebrushes	2019	Nets Hawk Katz Joshua Zahl
+	An Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications	2018	Pankaj K. Agarwal Boris Aronov Esther Ezra Joshua Zahl
+	An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³	2018	Nets Hawk Katz Joshua Zahl
+ PDF Chat	A discretized Severi-type theorem with applications to harmonic analysis	2018	Joshua Zahl
+ PDF Chat	Polynomial Wolff axioms and Kakeya-type estimates in R4	2018	Larry Guth Joshua Zahl
+	On the discretized sum-product problem	2018	Larry Guth Nets Hawk Katz Joshua Zahl
+ PDF Chat	Algebraic curves, rich points, and doubly-ruled surfaces	2018	Larry Guth Joshua Zahl
+ PDF Chat	Breaking the 3/2 Barrier for Unit Distances in Three Dimensions	2018	Joshua Zahl
+	An Efficient Algorithm for Generalized Polynomial Partitioning and Its Applications	2018	Pankaj K. Agarwal Boris Aronov Esther Ezra Joshua Zahl
+	On the discretized sum-product problem	2018	Larry Guth Nets Hawk Katz Joshua Zahl
+	Breaking the 3/2 barrier for unit distances in three dimensions	2017	Joshua Zahl
+ PDF Chat	A semi-algebraic version of Zarankiewicz's problem	2017	Jacob Fox János Pach Adam Sheffer Andrew Suk Joshua Zahl
+	An improved bound on the Hausdorff dimension of Besicovitch sets in $\mathbb{R}^3$	2017	Nets Hawk Katz Joshua Zahl
+	Cutting algebraic curves into pseudo-segments and applications	2017	Micha Sharir Joshua Zahl
+ PDF Chat	Point-Curve Incidences in the Complex Plane	2017	Adam Sheffer Endre Szabó Joshua Zahl
+	An improved bound on the Hausdorff dimension of Besicovitch sets in $\mathbb{R}^3$	2017	Nets Hawk Katz Joshua Zahl
+ PDF Chat	New bounds on curve tangencies and orthogonalities	2016	Jordan S. Ellenberg József Solymosi Joshua Zahl
+	New bounds on curve tangencies and orthogonalities	2016	Jordan S. Ellenberg József Solymosi Joshua Zahl
+ PDF Chat	Curves in $$\mathbb {R}^4$$ and Two-Rich Points	2016	Larry Guth Joshua Zahl
+ PDF Chat	Spectral gaps, additive energy, and a fractal uncertainty principle	2016	Semyon Dyatlov Joshua Zahl
+ PDF Chat	A NOTE ON RICH LINES IN TRULY HIGH DIMENSIONAL SETS	2016	Joshua Zahl
+ PDF Chat	A Szemerédi–Trotter Type Theorem in $$\mathbb {R}^4$$	2015	Joshua Zahl
+	A Szemerédi–Trotter Type Theorem in R[superscript 4]	2015	Joshua Zahl
+	Quantitative visibility estimates for unrectifiable sets in the plane	2015	M Bond Izabella Łaba Joshua Zahl
+	Algebraic curves, rich points, and doubly-ruled surfaces	2015	Larry Guth Joshua Zahl
+	Algebraic curves, rich points, and doubly-ruled surfaces	2015	Larry Guth Joshua Zahl
+	New bounds on curve tangencies and orthogonalities	2015	Jordan S. Ellenberg József Solymosi Joshua Zahl
+ PDF Chat	Few distinct distances implies no heavy lines or circles	2014	Adam Sheffer Joshua Zahl Frank de Zeeuw
+ PDF Chat	Improved Bounds for Incidences Between Points and Circles	2014	Micha Sharir Adam Sheffer Joshua Zahl
+	A semi-algebraic version of Zarankiewicz's problem	2014	Jacob Fox János Pach Adam Sheffer Andrew Suk Joshua Zahl
+	A semi-algebraic version of Zarankiewicz's problem	2014	Jacob Fox János Pach Adam Sheffer Andrew Suk Joshua Zahl
+	Few distinct distances implies no heavy lines or circles	2013	Adam Sheffer Joshua Zahl Frank de Zeeuw
+	An improved bound on the number of point-surface incidences in three dimensions	2013	Joshua Zahl
+ PDF Chat	Improved bounds for incidences between points and circles	2013	Micha Sharir Adam Sheffer Joshua Zahl
+	Quantitative visibility estimates for unrectifiable sets in the plane	2013	M Bond Izabella Łaba Joshua Zahl
+ PDF Chat	Improved bounds for incidences between points and circles	2013	Micha Sharir Adam Sheffer Joshua Zahl
+	Few distinct distances implies no heavy lines or circles	2013	Adam Sheffer Joshua Zahl Frank de Zeeuw
+ PDF Chat	$L^3$ estimates for an algebraic variable coefficient Wolff circular maximal function	2012	Joshua Zahl
+	Incidences between points and non-coplanar circles	2012	Micha Sharir Adam Sheffer Joshua Zahl
+ PDF Chat	On the Wolff circular maximal function	2012	Joshua Zahl
+	On the Wolff circular maximal function	2011	Joshua Zahl
+	An improved bound on the number of point-surface incidences in three dimensions	2011	Joshua Zahl
+	On the Wolff circular maximal function	2011	Joshua Zahl
+ PDF Chat	On universal cycles for multisets	2008	Glenn Hurlbert Tobias Johnson Joshua Zahl
+	Bounds on degrees of p-adic separating polynomials	2008	Daniel J. Katz Joshua Zahl
+	On Universal Cycles for Multisets	2007	Glenn Hurlbert Tobias Johnson Joshua Zahl
+	Universal Cycles on 3-Multisets	2006	Tobias Johnson Joshua Zahl
+	Universal Cycles on 3-Multisets	2006	Glenn Hurlbert Tobias Johnson Joshua Zahl

Common Coauthors

Coauthor	Papers Together
Adam Sheffer	14
Nets Hawk Katz	11
Micha Sharir	9
Esther Ezra	9
Larry Guth	8
Orit E. Raz	6
Boris Aronov	6
József Solymosi	5
Tobias Johnson	4
Jordan S. Ellenberg	3
Jacob Fox	3
Malabika Pramanik	3
Andrew Suk	3
Glenn Hurlbert	3
János Pach	3
Frank de Zeeuw	3
Jacob Denson	2
Izabella Łaba	2
Pankaj K. Agarwal	2
Jonathan E. Hickman	2
Shukun Wu	2
M Bond	2
Endre Szabó	1
Daniel Di Benedetto	1
Jonathan Hickman	1
Hong Wang	1
Hong Wang	1
Semyon Dyatlov	1
Tongou Yang	1
Pankaj K. Agarwal	1
Daniel J. Katz	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	On the Erdős distinct distances problem in the plane	2014	Larry Guth Nets Hawk Katz	23
+	Real algebraic geometry	2014	Jacek Bochnak Michel Coste Marie-Françoise Roy	22
+ PDF Chat	Combinatorial complexity bounds for arrangements of curves and spheres	1990	Kenneth L. Clarkson Herbert Edelsbrunner Leonidas Guibas Micha Sharir Emo Welzl	18
+ PDF Chat	An Incidence Theorem in Higher Dimensions	2012	József Solymosi Terence Tao	17
+ PDF Chat	Refined Bounds on the Number of Connected Components of Sign Conditions on a Variety	2011	Sal Barone Saugata Basu	16
+	Real Algebraic Geometry	1998	Frédéric Mangolte Jean-Philippe Rolin Kurdyka Krzysztof Saugata Basu Victoria Powers	15
+ PDF Chat	Recent work connected with the Kakeya problem	2003	Thomas Wolff	15
+	An improved bound on the number of point-surface incidences in three dimensions	2013	Joshua Zahl	13
+	On the Number of Incidences Between Points and Curves	1998	János Pach Micha Sharir	12
+ PDF Chat	Polynomial partitioning for a set of varieties	2015	Larry Guth	12
+ PDF Chat	Algebraic methods in discrete analogs of the Kakeya problem	2010	Larry Guth Nets Hawk Katz	12
+ PDF Chat	Bounds on Oscillatory Integral Operators Based on Multilinear Estimates	2011	Jean Bourgain Larry Guth	12
+ PDF Chat	An improved bound for Kakeya type maximal functions	1995	Thomas Wolff	11
+	Cutting algebraic curves into pseudo-segments and applications	2017	Micha Sharir Joshua Zahl	11
+ PDF Chat	On the Betti numbers of real varieties	1964	John Milnor	10
+	Extremal problems in discrete geometry	1983	Endre Szemerédi W. T. Trotter	10
+	On Sets of Distances of <i>n</i> Points	1970	P. Erdős	10
+	On the Erdos distinct distance problem in the plane	2010	Larry Guth Nets Hawk Katz	10
+ PDF Chat	Recent progress on the Kakeya conjecture	2002	N. Katz Terence Tao	10
+ PDF Chat	Volumes of tubular neighbourhoods of real algebraic varieties	1993	Richard Wongkew	10
+	Some connections between Falconer's distance set conjecture, and sets of Furstenburg type	2001	Nets Hawk Katz Terence Tao	10
+ PDF Chat	Polynomial Wolff axioms and Kakeya-type estimates in R4	2018	Larry Guth Joshua Zahl	10
+	The discretized sum-product and projection theorems	2010	Jean Bourgain	10
+ PDF Chat	Algebraic geometry: a first course	1993	Joe Harris	10
+ PDF Chat	Simple Proofs of Classical Theorems in Discrete Geometry via the Guth–Katz Polynomial Partitioning Technique	2012	Haim Kaplan Jiřı́ Matoušek Micha Sharir	10
+ PDF Chat	The endpoint case of the Bennett–Carbery–Tao multilinear Kakeya conjecture	2010	Larry Guth	10
+ PDF Chat	Unit Distances in Three Dimensions	2012	Haim Kaplan Jiřı́ Matoušek Zuzana Safernová Micha Sharir	10
+ PDF Chat	On the multilinear restriction and Kakeya conjectures	2006	Jonathan Bennett Anthony Carbery Terence Tao	9
+	Elementary Structure of Real Algebraic Varieties	1992	Hassler Whitney	9
+ PDF Chat	A Szemerédi–Trotter Type Theorem in $$\mathbb {R}^4$$	2015	Joshua Zahl	8
+	The Kakeya Maximal Function and the Spherical Summation Multipliers	1977	Antonio Cordóba	8
+ PDF Chat	On the polynomial Wolff axioms	2018	Nets Hawk Katz Keith M. Rogers	8
+ PDF Chat	Algebraic curves, rich points, and doubly-ruled surfaces	2018	Larry Guth Joshua Zahl	8
+ PDF Chat	Distinct Distance Estimates and Low Degree Polynomial Partitioning	2014	Larry Guth	7
+ PDF Chat	Non-Degenerate Spheres in Three Dimensions	2011	Roel Apfelbaum Micha Sharir	7
+	Some remarks on the Kakeya problem	1971	Roy O. Davies	7
+	On the size of Kakeya sets in finite fields	2008	Zeev Dvir	7
+ PDF Chat	A discretized Severi-type theorem with applications to harmonic analysis	2018	Joshua Zahl	7
+	How to find groups? (and how to use them in Erdős geometry?)	2012	György Elekes Endre Szabó	6
+	An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³	2018	Nets Hawk Katz Joshua Zahl	6
+ PDF Chat	An Improved Bound on the Minkowski Dimension of Besicovitch Sets in ℝ 3	2000	Nets Hawk Katz Izabella Łaba Terence Tao	6
+	Szemerédi–Trotter-type theorems in dimension 3	2014	Janós Kollár	6
+	Incidences of not-too-degenerate hyperplanes	2005	György Elekes Csaba D. Tóth	6
+ PDF Chat	Multilevel Polynomial Partitions and Simplified Range Searching	2015	Jiřı́ Matoušek Zuzana Patáková	6
+	Distinct distance estimates and low degree polynomial partitioning	2014	Larry Guth	5
+	Lower bounds for approximation by nonlinear manifolds	1968	Hugh E. Warren	5
+	A Treatise on the Analytic Geometry of Three Dimensions.	1959	F. N. David George Salmon C. H. Rowe	5
+ PDF Chat	Lenses in arrangements of pseudo-circles and their applications	2004	Pankaj K. Agarwal Eran Nevo János Pach Rom Pinchasi Micha Sharir Shakhar Smorodinsky	5
+	A restriction estimate using polynomial partitioning	2015	Larry Guth	5
+	Polynomial Methods in Combinatorics	2016	Larry Guth	5