Speaker
Description
Ordered structures that tile the plane in an aperiodic fashion - thus lacking translational symmetry - have long been considered in the mathematical literature. A general method for the construction of quasicrystals is known as cut-and-project ($\mathsf{CNP}$ for short), where an irrational slice "cuts" a higher-dimensional space endowed with a lattice and suitably chosen lattice points are further "projected down" onto the subspace to form the vertices of the quasicrystal. However, most of the known examples of $\mathsf{CNP}$ quasi-tilings are Euclidean. In this talk, after presenting the main ingredients of the Euclidean prescription, we will extend it to Lorentzian spacetimes and develop Lorentzian $\mathsf{CNP}$. This will allow us to discuss the first ever examples of Lorentzian quasicrystals, one in $(1+1)$- and another in $(1+3)$-dimensional spacetime. Finally, we will argue why the latter construction might be relevant for our Lorentzian spacetime. In particular, we shall appreciate how the picture of a quasi-crystalline spacetime could provide a potentially new string-compactification scheme that can naturally accommodate for the hierarchy problem and the smallness of our cosmological constant. Lastly, we will comment on its relevance to quantum geometry and quantum gravity; first, as a conformal Lorentzian structure of no intrinsic scale, and second through the connection of quasicrystals to quantum error-correcting codes.
| Presenter's Name | Sotirios Mygdalas |
|---|---|
| Presenter's Email Address | [email protected] |
| Keywords | Quasicrystals, Aperiodic Order, Reflection Groups, Lorentzian, Point Set, Compactifications, Conformal |
| Recording Permission | YES |
| Virtual Audience Permission | YES |
| Event Photography | I understand |
Author
Co-author
External references
- 25060084
- e935ff77-fd63-4d97-9adb-9412cf747e00
