Alex Cohen

I am an assistant professor at the Courant Institute of Mathematical Sciences, NYU. I currently hold a Clay Research Fellowship. I am interested in Fourier analysis, PDEs, combinatorics, and related fields.

CV here.   Email: alexcohen at nyu dot edu.   Office: Warren Weaver Hall 613.

Research

1. Moderate-doubling sets in $\mathbb{F}_2^n$ intersect subspaces
   with Dmitrii Zakharov, Submitted. (arXiv)
2. Counterexample to the two-ends Furstenberg conjecture in $\mathbb{R}^3$ (pdf)
3. A simple bound on fluctuations in the 3D Coulomb gas
   with Felipe Hernández, Submitted. (arXiv)
4. Sylvester-Gallai configurations on algebraic curves in $\mathbb{C}^2$
   Submitted. (arXiv)
5. Lower bounds for incidences
   with Cosmin Pohoata and Dmitrii Zakharov, Inventiones Mathematicae (2025). (journal, arXiv, Vimeo)
6. Clustering in typical unit-distance avoiding sets
   with Nitya Mani, Acta Mathematica Hungarica (2025). (journal, arXiv)
7. A new upper bound for the Heilbronn triangle problem
   with Cosmin Pohoata and Dmitrii Zakharov, Submitted. (arXiv, Quanta, Blog, YouTube)
8. Fractal uncertainty in higher dimensions
   Annals of Mathematics (2025). (journal, arXiv, YouTube)
9. Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial
   with Lior Alon and Cynthia Vinzant, Journal of Functional Analysis (2024). (journal, arXiv)
10. Fractal uncertainty for discrete 2D Cantor sets
    Analysis and PDE (2025). (journal, arXiv)
11. Partition and Analytic Rank are Equivalent over Large Fields
    with Guy Moshkovitz, Duke Mathematical Journal (2023). (journal, arXiv, Quanta, YouTube)
12. Uniqueness of excited states to $-\Delta u + u - u^3 = 0$ in three dimensions
    with Zhenhao Li and Wilhelm Schlag, Analysis & PDE (2024). (journal, arXiv, GitHub)
13. Structure vs. randomness for bilinear maps
    with Guy Moshkovitz, Discrete Analysis (2022), presented at Symposium on Theory of Computing (2021). (journal, arXiv, YouTube)
14. A Sylvester-Gallai result for concurrent lines in the complex plane
    Discrete and Computational Geometry (2020). (journal, arXiv)
15. A Sylvester-Gallai theorem for cubic curves
    with Frank de Zeeuw, European Journal of Combinatorics (2022). (journal, arXiv)
16. Poissonian correlation of higher order differences
    Journal of Number Theory (2021). (journal, arXiv)
17. Sinkhorn limits in finitely many steps
    with Melvyn Nathanson, Linear Algebra and its Applications (2019). (journal, arXiv)

Expository / Notes

• Lecture notes on lower bounds for incidences (notes)
• A table of incidence bounds written different ways (table)
• Talk notes on discrete and continuous projections in $\mathbb{R}^2$ (notes, talk)
• Lecture notes on the Kakeya conjecture (notes, pset, rigorous proof)
• Conjecture about p-adic fractal uncertainty (note)
• PhD thesis on the Fractal Uncertainty Principle (thesis)
• Undergrad senior essay on Gauss–Bonnet–Chern (pdf)

Slides

• Branching functions in phase space (slides)
• Turing's theory of morphogenesis (slides)
• Incidence lower bounds (slides)
• Higher dimensional fractal uncertainty (slides)
• Heilbronn's triangle problem and connections to projection theory (slides)
• Fractal uncertainty for discrete 2D Cantor sets (slides)
• Partition rank vs. analytic rank of tensors (slides)
• A Sylvester-Gallai theorem for concurrent lines in the complex plane (slides)
• A circle of ideas around the Gauss-Bonnet theorem (slides)