Given a type of object, a common goal in mathematics is to classify them. Geometry aims to do this via a moduli space, a parameter space for the objects that "reflects the geometric data in some nice way". Such hand-wavy intuition turns out to be hard to define, and spaces often become incredibly messy very quickly. As a result, the study of moduli spaces has a (kind of fair) reputation as an impenetrable mess. In this talk, we'll cut through the formal definitions with lots of concrete examples and give some insight into why such spaces can very quickly spiral out of hand. We'll conclude with an example of a particularly nice (ie. drawable) moduli space: the space of metric trees.
A Friendly Introduction to Moduli Spaces
Tue, 10/10/2017 - 12:00