This is Fabian Müller's talk "What is ... a moduli space?" at the "What is ...?" seminar. The talk was given on Friday, June 10, 1:00pm at the BMS Loft at Urania.
In modern algebraic geometry, moduli spaces provide a way of describing the set of isomorphism classes of various kinds of objects, such as curves, maps or vector bundles. While the points of the moduli space correspond just to these isomorphism classes, these spaces can be endowed with a much richer algebraic structure reflecting the way in which the objects under consideration behave in families.
The talk will give a low-level introduction to the concepts of fine and coarse moduli spaces, classifying maps and universal families. With an eye towards the subsequent talk by Valery Alexeev, we will also take a short look at the issues one encounters when one tries to compactify such spaces.
For more "What is ...?" seminar videos, visit math.fu-berlin.de/w/Math/WhatIsSeminar.