Izabella Łaba (University of British Columbia, Canada), Tiling the integers with translates of one tile, and connections to harmonic analysis

Oddział Warszawski Polskiego Towarzystwa Matematycznego 

W dniu 16 marca 2022 roku (ŚRODA) o godz. 18:00 w ramach cyklu Poznajmy się - przypomnijmy się sobie nawzajem

Profesor Izabella Łaba (Department of Mathematics University of British Columbia, Vancouver, Canada)

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TILING THE INTEGERS WITH TRANSLATES OF ONE TILE, AND CONNECTIONS TO HARMONIC ANALYSIS

Abstrakt:

It is well known that if a finite set of integers A tiles the integers by translations, then the translation set must be periodic, so that the tiling is equivalent to a factorization A+B=Z_M of a finite cyclic group. Coven and Meyerowitz (1998) proved that when the tiling period M has at most two distinct prime factors, each of the sets A and B can be replaced by a highly ordered "standard" tiling complement. It is not known whether this behaviour persists for all tilings with no restrictions on the number of prime factors of M. 
In joint work with Itay Londner, we proved that this is true for tilings of period M=(pqr)², where p, q, r are distinct primes. I will discuss the main ideas of the proof, and connections to questions in harmonic analysis such as Fuglede's spectral set conjecture and Favard length estimates for fractal sets.

                                                                                                                                                                                                             Izabella Łaba

Link do spotkania na platformie Zoom:
https://us02web.zoom.us/j/83952146293?pwd=eC9MM0hPM3RBa2ZBSWt4eGEzL0NXdz09 [2]

Meeting ID: 839 5214 6293
Passcode: PTM
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