Speaker: Dr Klara Stokes, Maynooth University Department of Electronic Engineering
Title: "Voltages, flows, divisors and specials points on (network) graphs"
Abstract: (Combinatorial) graphs can be seen as mathematical models of networks. A voltage graph is a graph with voltages at the edges. In mathematics, the voltages of a voltage graph are taken from a (mathematical) group. It was proved by Gross and Tucker in the 1977 that any (nice) graph cover can be described by a voltage graph with permutation voltages. Voltage graphs are very useful, because they can transform a problem on a large graph (the covering graph) to a problem on a small graph (the base graph).
In Baker-Norine theory, the graph is treated as if it was an algebraic curve. The theory uses concepts like flows and divisors on graphs. Several results about algebraic curves have been translated to the context of graph theory in this context. I will talk about Weierstrass points on graph, and what we can say about them in relation to graph covers.