This is a preview. Log in through your library . Abstract We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the ...

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.

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, ...

The Kaplansky conjectures are three long-standing open problems on the group rings of torsion-free groups. Last week, Dr. Giles Gardam, postdoc in Mathematics Münster's topology group, announced that ...