Fakulta matematiky, fyziky
a informatiky
Univerzita Komenského v Bratislave

Algebraic Graph Theory International Webinar (30.5.2023)

v utorok 30.5.2023 o 19:00 hod.

29. 05. 2023 15.16 hod.
Od: Róbert Jajcay

The organizers of the Algebraic Graph Theory International Webinar would like to invite you to join us and other colleagues on May 30, 2023, at 7pm Central European Summer Time (= 5pm UTC, please note that we switched to summer time), for the next presentation delivered by Chaim Goodman-Strauss. 

The title: An aperiodic monotile

A longstanding open problem asks for an aperiodic monotile, also known as an "einstein": a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons. We first show that a representative example, the "hat" polykite, can form clusters called "metatiles", for which substitution rules can be defined. Because the metatiles admit tilings of the plane, so too does the hat. We then prove that generic members of our continuum of polygons are aperiodic, through a new kind of geometric incommensurability argument. Separately, we give a combinatorial, computer-assisted proof that the hat must form hierarchical -- and hence aperiodic -- tilings. This is joint work with

David Smith, Joseph Samuel Myers, and Craig S. Kaplan.

The Zoom link for this semester is:

Meeting ID: 871 9332 0713
Passcode: 653250

Further details may be found at http://euler.doa.fmph.uniba.sk/AGTIW.html

where you can also find the slides and the recordings of our previous presentations. Also, if you wish to advertise an AGT friendly conference on this page, please send us the link.  

Hoping to see you at the webinar, and wishing you all the best. 

Isabel HubardRobert Jajcay and Primoz Potocnik