Title: An Introduction to the Moduli Space of Curves
Speaker: Andy Yang
Abstract: The moduli space of curves parametrizes all smooth algebraic curves of a fixed genus up to isomorphism and plays a central role in many areas of geometry. In this talk, I will introduce the basic philosophy of moduli spaces through concrete examples and focus on the geometry of these spaces. We will discuss how different geometric phenomena such as degeneration, deformation, and stratification naturally appear in this setting. I will also describe the Teichmüller-theoretic viewpoint on moduli spaces. If time permits, I will end with a short glimpse of tautological classes.
Some snacks will be provided before and after the talk.