## This Week

#### Lior Tenenbaum (*Technion*)

Periodic approximation of substitution subshifts

Periodic approximation of substitution subshifts

In studying higher dimensional Schrödinger operators of quasicrystals, one is lead to find suitable periodic approximations. This means in particular that the spectrum converges as a set to the limiting spectrum. It turns out that for this to hold, the convergence of the underlying dynamical systems is exactly what is needed. This is the starting point of the present talk.

We focus on aperiodic subshifts defined through symbolic substitutions. These substitution subshifts provide models of aperiodic ordered systems. We find natural sequence candidate of subshifts to approximate the aforementioned substitution subshift. We characterize when these sequences converge, and if so at what asymptotic rate. Some well-known examples of substitution subshifts are discussed during the talk. We will also discuss the motivation for this characterization, arising from an attempt to study higher dimensional quasi-crystals. This is based on a Joint work with Ram Band, Siegfried Beckus and Felix Pogorzelski.

## 2023–24–B meetings

### Upcoming Meetings

Date |
Title |
Speaker |
Abstract |
---|---|---|---|

May 30 | Periodic approximation of substitution subshifts | Lior Tenenbaum (Technion) | |

Jun 13 | TBA | Gill Goffer (UCSD) | |

Jun 27 | TBA | Ilya Gekhtman (Technion) |

### Past Meetings

Date |
Title |
Speaker |
Abstract |
---|---|---|---|

May 9 | Higher Kazhdan Property and Unitary Cohomology of Arithmetic Groups | Uri Bader (BGU) | |

May 16 | Equidistribution of Discrepancy Sequences (Joint with Dolgopyat) | Omri Sarig (Weizmann Institute of Science) | |

May 23 | Random temporo-spatial differentiations | Adian Young (BGU) |

Seminar run by Dr. Shrey Sanadhya and Dr. Ido Grayevsky