Colloquium information

Special Colloquium

Spectral properties of the Laplace operator on some periodic graphs

Speaker:  Eugenia Malinnikova (University of Stanford)
Date:  Thursday, 25 June 2026 - 12:00
Place:  Aula Naranja, ICMAT

Abstract:

First, known results on the spectra of universal covers of finite graphs will be reviewed. Particular attention will be given to a theorem of Avni, Breuer, and Simon, which rules out singular continuous spectrum in that setting. Then we will show that this absence of singular continuous spectrum extends to a large class of more general periodic covering graphs and discuss the absolutely continuous and pure point parts of the spectrum.

The talk will conclude with several examples of periodic covering graphs for which the spectrum can be computed explicitly.

This is a work in progress with Theo McKenzie and Stanislav Krymskii.

Poster