##### Department of Mathematics,

University of California San Diego

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### Math 211 - Group Actions Seminar

## Rachel Greenfeld

#### UCLA

## Translational tilings in lattices

##### Abstract:

Let $F$ be a finite subset of $\mathbb{Z}^d$. We say that $F$ is a translational tile of $\mathbb{Z}^d$ if it is possible to cover $\mathbb{Z}^d$ by translates of $F$ without any overlaps. The periodic tiling conjecture, which is perhaps the most well-known conjecture in the area, suggests that any translational tile admits at least one periodic tiling. In the talk, we will motivate and discuss the study of this conjecture. We will also present some new results, joint with Terence Tao, on the structure of translational tilings in lattices and introduce some applications.

Host: Brandon Seward

### April 20, 2021

### 10:00 AM

### Zoom ID 967 4109 3409 (email Nattalie Tamam or Brandon Seward for the password)

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