Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.

In the first (theoretical) part of this paper, we prove a number of constraints on hypothetical counterexamples to the Casas-Alvero conjecture, building on ideas of Graf von Bothmer, Labs, Schicho and ...

Given a nonempty compact connected subset $X\subset {\Bbb S}^{2}$ with complement a simply-connected open subset $\Omega \subset {\Bbb S}^{2}$, let Dome(Ω) be the ...

But they’re related. Greenfeld and Tao planned to come up with a discrete counterexample to the conjecture that they could then modify to work in the continuous case as well. In the summer of 2021, ...

Mathematicians from New York University and the University of British Columbia have resolved a decades-old geometric problem, the Kakeya conjecture in 3D, which studies the shape left behind by a ...

Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future. In May, a ...

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...