# Mustazee Rahman: On local geometry and spectrum of graphs

**Time: **
Tue 2019-03-12 15.15 - 16.15

**Location: **
Room F11 KTH

**Participating: **
Mustazee Rahman (KTH)

Abstract: The spectrum of a matrix is like its soul while the kernel is the body. An old question, of course, is how much of a body is remembered by the soul. Metaphors aside, I will speak about how the spectrum of big graphs determine their local geometry around typical vertices and the relationship between spectra and density of short cycles. For instance, certain graphs can be identified by the spectral radius alone. Along the way there will be connections to non-backtracking walks, entropy, graph limits and amenability.