Alex Cohen

I am a fourth year graduate student at MIT studying harmonic analysis. My advisor is Larry Guth.

Starting September 2025 I will be an assistant professor at Courant Institute of Mathematical Sciences, NYU. I will also be a Clay Research Fellow starting in 2025.

I am interested in Fourier analysis, PDEs, combinatorics, and related fields.

My CV can be found here. My email is alexcoh at mit dot edu.

Research

• Lower bounds for incidences
  with Cosmin Pohoata and Dmitrii Zakharov, to appear in Inventiones Mathematicae. (journal, arXiv, Vimeo).

• Clustering in typical unit-distance avoiding sets
  with Nitya Mani, Submitted. (arXiv).

• A new upper bound for the Heilbronn triangle problem
  with Cosmin Pohoata and Dmitrii Zakharov, Submitted. (arXiv, Quanta, Blog post, YouTube).

• Fractal uncertainty in higher dimensions
  to appear in Annals of Mathematics. (journal, arXiv, YouTube).

• 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).

• Fractal uncertainty for discrete 2D Cantor sets
  to appear in Analysis and PDE. (journal, arXiv).

• Partition and Analytic Rank are Equivalent over Large Fields
  with Guy Moshkovitz, Duke Mathematical Journal (2023). (journal, arXiv, Quanta, YouTube).

• 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).

• Structure vs. randomness for bilinear maps
  with Guy Moshkovitz, Discrete Analysis (2022), presented at Symposium on Theory of Computing (2021). (journal, arXiv, YouTube).

• A Sylvester-Gallai result for concurrent lines in the complex plane
  Discrete and Computational Geometry (2020). (journal, arXiv).

• A Sylvester-Gallai theorem for cubic curves
  with Frank de Zeeuw, European Journal of Combinatorics (2022). (journal, arXiv).

• Poissonian correlation of higher order differences
  Journal of Number Theory (2021). (journal, arXiv).

• Sinkhorn limits in finitely many steps
  with Melvyn Nathanson. Linear Algebra and its Applications (2019). (journal, arXiv).

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)

Here is a list of properties of the Fourier transform.