An aperiodic monotile

It is finally done – the long standing question whether there exists a single tile that can cover the entire plane, but only aperiodically, is answered! Here is the answer (arXiv:2303.10798): Many other people have already written blog posts, etc. about this, hence I will refrain from repeating everything and just refer to those other … Continue reading "An aperiodic monotile"

Abel Prize 2023

The Able Prize 2023 is awarded to Luis A. Caffarelli for his seminal contributions to regularity theory for nonlinear partial differential equations including free-boundary problems and the Monge–Ampère equation.

Coherence of one-relator groups

The recent series of results about one-relator groups (see, e.g. the previous two blog posts) culminates now in the final breakthrough: The conjecture of Baumslag from the 70s (that all one-relator groups are coherent) is resolved. The corresponding preprint by Marco Linton was put today on the arXiv:2303.05976.