- Series
- School of Mathematics Colloquium
- Time
- Friday, October 25, 2024 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005/006
- Speaker
- Peter Sarnak – Princeton University – sarnak@math.princeton.edu – https://www.math.princeton.edu/people/peter-sarnak
- Organizer
- Alexander Dunn
Endowing a finite combinatorial graph with lengths on its edges defines singular 1-dimensional Riemannian manifolds known as metric graphs. The spectra of their Laplacians have been widely studied. We show that these spectra have a structured linear part described in terms of arithmetic progressions and a nonlinear "random" part which is highly linearly and even algebraically independent over the rationals. These spectra give rise to exotic crystalline measures ("Generalised Poisson Summation Formulae") and resolve various open problems concerning the latter. This is a joint work with Pavel Kurasov.