Alex Cohen

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

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

• 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
  Submitted. (arXiv).

• Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial
  with Lior Alon and Cynthia Vinzant, to appear in Journal of Functional Analysis. (arXiv).

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

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

• Uniqueness of excited states to $-\Delta u + u - u^3 = 0$ in three dimensions
  with Zhenhao Li and Wilhelm Schlag, to appear in Analysis & PDE. (arXiv, GitHub).

• Structure vs. randomness for bilinear maps
  with Guy Moshkovitz, to appear in Discrete Analysis, 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

• 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.