The problem Heikkilä solved concerns the classification of quasiregularly elliptic 4-manifolds, which involves understanding which four-dimensional spaces can be formed by deforming standard ...

invariant features exhibit high robustness to viewpoint changes by purely encoding the geometry information. Second, equivariant features in latent space, which encode the pose information, are more ...

asking what four-dimensional shapes can be obtained by deforming four-dimensional Euclidean geometry. The article by Heikkilä and Pekka Pankka has been published in the Annals of Mathematics journal.

Traditional models of cosmic creation often involve Euclidean space—a phase where ... imagines a universe emerging from a smooth, compact geometry, yet it typically predicts too few inflationary ...

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 ...