# Pavel Kurasov: Graph Laplacians - secular polynomials, reducibility and arithmetic properties of the spectrum

**Time: **
Wed 2020-03-04 13.15 - 15.00

**Location: **
Kräftriket, house 6, room 306 (Cramér-rummet)

**Lecturer: **
Pavel Kurasov, Stockholms universitet

### Abstract

To determine spectra of Laplacians on metric graphs one may use multivariable polynomials, called secular polynomials. They are hyperbolic in the sense that their zero sets belong to the N-dimensional torus and intersections with any line on the torus is asymptotically linear. We discuss how the secular polynomials change when the graph is amended, as well as their reducibility and when their zero sets contain tori of co-dimension one. As a result of this analysis we describe spectral properties of graph Laplacians and corresponding spectral measures.

This is a joint work with Peter Sarnak.