The goal of this paper is to motivate the construction of moduli spaces through a few key examples — the moduli space of complex elliptic curves and the moduli space of triangles.

Last time we discussed the example of the moduli functor of families of vector spaces of rank n. In the following two lectures, we will take a step back and discuss the general formalism of sheaves of …

One of the most desirable properties of a moduli space is the existence of a universal family (see §1.3.4), and the presence of automorphisms obstructs its existence(see§1.3.5).

1.1 Motivating examples Before diving in, I want to give some motivating examples of works that crucially relied on the tools and techniques of moduli theory. Many of the moduli theoretic ideas that …

The following are the lecture notes for a course about the moduli space of stable curves given in the Summer of 2020 at the University of Bonn. In the course, we de ne the moduli space and discuss its …

We will tackle this question by introducing moduli spaces of stable maps, and we will sketch the proof of Kontsevich using Gromov-Witten invariants. Before we do so though, I want to go back to Q3, where …

In this course, I would like to present the basic ideas and formalism underlying the concept of moduli space, along with some main examples of interdisciplinary interest.