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 ...

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.

Proceedings of the American Mathematical Society, Vol. 81, No. 2 (Feb., 1981), pp. 193-194 (2 pages) In [5] Swarup states a group theoretic conjecture P2 and shows that $\mathrm{P1} \Rightarrow ...

Chinese mathematician Wang Hong has solved an “infamous” geometry problem called the Kakeya conjecture within three dimensions. It is considered a breakthrough that could have implications for imaging ...