Joshua Zahl
Current position
2025.06 - Professor, Chern Institute of Mathematics, Nankai University
Previous positions
2021.03 - 2025.06 Associate professor, University of British Columbia, Canada
2016.06 - 2021.03 Assistant professor, University of British Columbia, Canada
2013.09 - 2016.05 NSF/pure math instructor, Massachusetts Institute of Technology, USA
Education background
2010.08 - 2013.08 PhD, University of California, Los Angeles, USA
2008.09 - 2010.07 MSc, University of California, Los Angeles, USA
2004.09 - 2008.06 BSc, California Institute of Technology, USA
Selected publications
1. A Szemeredi-Trotter type theorem in R^4
Discrete. Comput. Geom. 2015
2. Spectral gaps, additive energy, and a fractal uncertainty principle
with Semyon Dyatlov. Geom. Funct. Anal. 2016
3. New bounds on curve tangencies and orthogonalities
with Jordan Ellenberg, Jozsef Solymosi. Discrete Analysis 2016
4. A semi-algebraic version of Zarankiewicz's problem
with Jacob Fox, Janos Pach, Andrew Suk, Adam Sheffer. J. Eur. Math. Soc. 2017
5. Cutting algebraic curves into pseudo-segments and applications
with Micha Sharir, J. Combin. Theory Ser. A 2017
6. A discretized Severi-type theorem with applications to harmonic analysis
Geom. Funct. Anal. 2018
7. Point-curve incidences in the complex plane
with Endre Szabo, Adam Sheffer. Combinatorica. 2018
8. Algebraic curves, rich points, and doubly-ruled surfaces
with Larry Guth. Amer. J. Math. 2018
9. Polynomial Wolff axioms and Kakeya-type estimates in R^4
with Larry Guth, Proc. London Math. Soc. 2018
10. An improved bound on the Hausdorff dimension of Besicovitch sets in R^3
with Nets Katz, J. Amer. Math. Soc. 2019
11. Breaking the 3/2 barrier for unit distances in three dimensions
Int. Math. Res. Not. 2019
12. New Kakeya estimates using Gromov's algebraic lemma
Adv. Math. 2021
13. On the discretized sum-product problem
with Larry Guth, Nets Katz, Int. Math. Res. Not. 2021
14. Distinct distances in the complex plane
with Adam Sheffer. Trans. Amer. Math. Soc. 2021
15. Sphere tangencies, line incidences, and Lie's line-sphere correspondence
Math. Proc. Camb. Philos. Soc. 2022
16. Unions of lines in R^n
Mathematika 2023
17. On the dimension of exceptional parameters for nonlinear projections, and the discretized Elekes-Rónyai theorem
with Orit Raz. Geom. Funct. Anal.2024.
18. Improved Elekes-Szabó type estimates using proximity
with Jozsef Solymosi. J. Comb. Theory Ser. A. 2024
19. The Assouad dimension of Kakeya sets in R^3
with Hong Wang. Invent. Math. 2025.
20. On Maximal Functions Associated to Families of Curves in the Plane
Duke Math J. 2025+.
21. A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in R^3
with Malabika Pramanik, Tongou Yang. Amer. J. Math. 2025+
Student supervision
1. Daniel De Benedetto, PhD 2017 - 2021. 2022+ working at Pythia Sports
2. Jacob Denson, MSc 2017-2019. 2019+ PhD student at UW Madison
3. Kyle Chi Hoi Yip, MSc 2019-2021, PhD 2021-2024. 2024+ postdoc at Georgia Tech
4. Mukul Rai Choudhuri, MSc 2019-2021, PhD 2021-2025. 2025+ Postdoc at University of Georgia
5. Kenneth Moore, PhD 2021 - 2025. 2025+ Postdoc at the Rényi Institute
6. Andrew Alexander, MSc 2023 - 2025, PhD 2025 - present
7. Paige Bright, MSc 2024 - 2025. 2025+ PhD student at MIT
8. Chenjian Wang, PhD 2025 - present
Postdoctoral supervision
1. Orit Raz, 2017-2019. 2019+ faculty at the Hebrew University of Jerusalem
2. Itay Londner, 2018-2021. 2021+ postdoc at the Weizmann Institute of Science
3. Tongou Yang, 2021-2022. 2025+ Assistant Professor, Southern University of Science and Technology
4. William O'Regan, 2024 - present
Office：Room 613, Shiing-Shen Building
Email：jzahl@nankai.edu.cn
