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…