5 citations · 12 across the 6 of their papers we have counts for
12 papers
A 1/64 spectral gap for surfaces with
Alex Cohen, Semyon Dyatlov
We show that any convex co-compact hyperbolic surface with exponent of convergence of Poincaré series has an essential spectral gap of size $β=\tfrac…
Sylvester--Gallai configurations on algebraic curves in C^2
Alex Cohen
The Sylvester-Gallai theorem says that for any finite set of non-collinear points in , there is some line passing through exactly two points of the set. Over the complex numb…
A new upper bound for the Heilbronn triangle problem
Alex Cohen, Cosmin Pohoata, Dmitrii Zakharov
For sufficiently large , we show that in every configuration of points chosen inside the unit square there exists a triangle of area less than . This improv…
Fractal uncertainty in higher dimensions
Alex Cohen
We prove that if a fractal set in avoids lines in a certain quantitative sense, which we call line porosity, then it has a fractal uncertainty principle. The main in…
Every real-rooted exponential polynomial is the restriction of a Lee-Yang polynomial
Lior Alon, Alex Cohen, Cynthia Vinzant
A Lee-Yang polynomial is a polynomial that has no zeros in the polydisc and its inverse $ (\mathbb{C}\setminus\overline{\mathbb{D}})^{n…
Fractal uncertainty for discrete 2D Cantor sets
Alex Cohen
We prove that a self-similar Cantor set in has a fractal uncertainty principle if and only if it does not contain a pair of orthogonal lines. The…
Partition and Analytic Rank are Equivalent over Large Fields
Alex Cohen, Guy Moshkovitz
We prove that the partition rank and the analytic rank of tensors are equal up to a constant, over finite fields of any characteristic and any large enough cardinality depending on…
Structure vs. Randomness for Bilinear Maps
Alex Cohen, Guy Moshkovitz
We prove that the slice rank of a 3-tensor (a combinatorial notion introduced by Tao in the context of the cap-set problem), the analytic rank (a Fourier-theoretic notion introduce…
A Sylvester-Gallai theorem for cubic curves
Alex Cohen, Frank de Zeeuw
We prove a variant of the Sylvester-Gallai theorem for cubics (algebraic curves of degree three): If a finite set of sufficiently many points in is not contained in…
A Sylvester-Gallai result for concurrent lines in the complex plane
Alex Cohen
We show that if a set of points in lies on a family of concurrent lines, and if one of those lines contains more than points, then there is a line passing…
Poissonian correlation of higher order differences
Alex Cohen
A sequence on the torus exhibits Poissonian pair correlation if for all , \begin{equation*} \lim_{N\to\infty} \frac{1}{N}\#\left\{1\leq…
Sinkhorn limits in finitely many steps
Alex Cohen, Melvyn B. Nathanson
Applied to a nonnegative matrix with a nonzero -diagonal, the sequence of matrices constructed by alternate row and column scaling conveges to a doubly stochastic ma…