Yueqi Cao: Computing the Tropical Abel-Jacobi Transform of Metric Graphs

Abstract.

Metric graphs are widely used to model complex real-world data. The problem of how to extract and represent the geometric and topological information from graph data has given rise to various research areas, such as graph representation learning and graph reconstruction. Despite the immense literature in machine learning, the representation of metric graphs as abstract tropical curves has never been studied previously in computational and machine learning contexts. In this talk, I will introduce the tropical Abel--Jacobi transform of metric graphs and present algorithms for computation. Then I will discuss potential applications of the tropical Abel--Jacobi transform to graph embedding and topological data analysis.