Abstract:
Graphs and their Laplace operators play an important role in various different branches of mathematics (e.g. combinatorics, data science, group theory). A key observation is that many structural properties of a graph are closely related to the spectrum of its Laplace operator.
Consequently, understanding the spectrum of graph Laplacians has become an important topic with connections to several other fields.
In this talk, we will first introduce Laplace operators on graphs and then present some aspects of this theory (including random walks on graphs, Cayley graphs and quantum graphs).