28 feb 2025 -- 11:15   [open in google calendar]

Centro de Giorgi, Sala Conferenze

Abstract.

In this talk, aimed at a non-specialist audience, we introduce the concept of moduli in algebraic geometry, explain why algebraic geometers are interested in the study of moduli spaces, and begin to indicate the challenges involved in proving that moduli spaces exist in the first place. We also begin to explain how the notion of stability in algebraic geometry is related to the existence of moduli spaces, focusing in particular on the moduli space of semistable vector bundles on a smooth projective algebraic curve. At the end of the talk I will briefly report on work in progress, joint with L. Modin, about the existence of moduli spaces of unstable objects in Abelian categories, generalising results of Jackson, Hoskins—Jackson and Qiao concerning the existence of moduli spaces of unstable coherent sheaves on projective varieties, and of Hamilton concerning the existence of moduli spaces of unstable Higgs bundles on a smooth projective curve.