Anders Karlsson (Université de Genève)

"Spanning trees and heights of tori"

The number of spanning trees of a finite graph is called the complexity and is an important invariant also outside of mathematics. Using heat kernel methods we obtain rather precise asympotics for the complexity of certain discretizations of real tori. A constant appearing in this asymptotic formula is the height of the corresponding real torus. This number is the derivative at 0 of a spectral zeta function and is known to be expressible in terms of modular forms. Conjecturally it is also related to regular sphere packings. Joint work with G. Chinta and J. Jorgenson.