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 ...
Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528-1577 Amer. Math. Soc] proposed two general conjectures about repeated games: the first one ...
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 ...
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