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Moduli Spaces of GraphsFinite metric graphs represent processes and objects in many different areas of mathematics and science, so one would like to understand the set of all graphs relevant to a given problem, i.e. the moduli space of such graphs. In this talk I will highlight some recent progress in the study of moduli spaces of graphs, first reviewing historical developments that have led up to them. I will concentrate on moduli spaces of graphs with a specified fundamental group, and explain how the study of such spaces both contributes to and profits from the theory of outer automorphism groups of free groups. Finally, I will mention connections with the classical symmetric space of lattices in Euclidean space, with Kontsevich’s graph complexes and with the algebraic geometers’ moduli space of tropical curves.Uploaded 09-09-26The ICM Emmy Noether Lecture honors women who have made fundamental and sustained contributions to the mathematical sciences. The ICM Emmy Noether Lecture is named after the German mathematician Emmy Noether. Since 2006, this lecture is a permanent ICM tradition, since 2014, a special commemorative plaquette is given to each ICM Emmy Noether Lecturer. Learn more about your ad choices. Visit megaphone.fm/adchoices
