Harmonic morphisms of graphs
Roman Nedela


Abstract

In analogy with complex analysis and Riemann geometry, we introduce and investigate properties of graph coverings and their generalisations - harmonic morphisms. While graph coverings correspond to smooth coverings between surfaces, the concept of a harmonic morphism is a counterpart to the concept of a branched covering between surfaces.

While coverings of graphs were succesfully used in graph theory, in particular as a powerful construction method, harmonic morphisms are less known in the community. We briefly mention main applications of coverings and explain the potential of harmonic morphisms in connection with Jacobians of graphs. In the end of the talk we mention recent results of the speaker about the Riemann-Hurwitz-like theorems for graphs.