# AGA

## Seminar

### Heat kernels on metric graphs and a trace formula

Seminar Room 1, Newton Institute

#### Abstract

We report on joint work with V. Kostrykin and J. Potthoff. On metric graphs and for a certain class of Laplace operators a representation for the heat kernel in terms of walks is given. This representation is obtained from a corresponding one for the resolvent derived previously by two of the authors. This results in a Selberg-Gutzwiller type formula for the trace and extends earlier results by other authors in the context of quantum graphs.

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