# Workshop on Additive Combinatorics and Algebraic Connections

## The Failure of the Periodic Tiling Conjecture

Abstract: Translational tiling is a covering of a space using translated copies of a building block, called a "tile", without any positive measure overlaps. What are the possible ways that a space can be tiled?

The most well known conjecture in this area is the periodic tiling conjecture. It asserts that any tile of an Euclidean space admits a periodic tiling. This conjecture was first posed over 30 years ago and has been intensively studied over the years. In a joint work with Terence Tao, we prove the failure of the periodic tiling conjecture. In the talk, I will motivate this result and discuss our proof.

### Date & Time

October 24, 2022 | 2:00pm – 3:00pm

### Location

Simonyi 101 and Remote Access### Speakers

### Affiliation

Member, School of Mathematics