Title: The structure of translational tilings
Speaker: Rachel Greenfeld
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?Date: Monday, January 09, 2023
One of the most well known conjectures in this area is the periodic tiling conjecture. It asserts that any tile of Euclidean space admits a periodic tiling. This conjecture was posed over 30 years ago and has been intensively studied over the years. In a joint work with Terence Tao, we disprove the periodic tiling conjecture in high dimensions. In the talk, I will motivate this result and discuss our proof.