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        "event_title":"Student Algebraic Geometry: The Valuative Tree, Part 1",
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        "combined_title":"Student Algebraic Geometry: The Valuative Tree, Part 1: Benjamin Baily",
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        "description":"Consider the set of valuations v: C[[x,y]] -> R \\cup \\{\\infty\\}, normalized so that min(v(x), v(y)) = 1. We'll show that this set naturally has the structure of a metric tree. This insight allows us to study the singularities of ideals, graded systems of ideals, and plurisubharmonic functions in a unified way. \r\n\r\nThis talk will serve as an introduction to the valuative tree, following Favre-Jonsson. We'll focus on the basic structure of the tree and numerical invariants of valuations with examples.",
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