Department seminar: "Tiling n-Space by Unit Cubes"

Abstract:

"In 2016 I gave in your seminar a talk entitled “Conjectures and Open Questions in Mathematics”.  As the talk seemed to be received well, I will talk again about conjectures and open questions; this time the topic will be restricted to Discrete Geometry and Error-correcting-codes.

Tiling problems belong to the oldest problems in mathematics. They attracted attention of many famous mathematicians. Even one of the Hilbert's problems is devoted to the topic.

The interest in tilings by unit cubes originated with a conjecture raised by Minkowski in 1907, which claims that every lattice tiling of n-space by unit cubes must contain a pair of twin cubes.

We discuss this conjecture, its history, variations, and then describe some problems that Minkowski’s conjecture, in turn, suggested, e.g. the conjecture of Keller. The Golomb-Welch conjecture, the long-standing, and the most famous conjecture in error-correcting codes in Lee metric, will be discussed in great detail."

Refreshments will be served after the talk.