What is… a moduli space?

André Oliveira, CMUP & UTAD, Portugal

19 de maio de 2021, às 16h no endereço Zoom:

https://videoconf-colibri.zoom.us/j/83030580321?pwd=Z3VLNjc0c3VXUHNqQWtLN1ZPaHY1QT09

ID: 830 3058 0321 | Palavra chave: xyz

Resumo/Abstract: Mathematicians like to classify and organize mathematical objects, up to some fixed equivalence relation. Sometimes the objects in question do not admit continuous variations and so the classification is given by discrete invariants. But many other times, especially for objects coming from algebraic geometry, the objects admit such variations. Then they are classified by what is known as a moduli space. It turns out that many moduli spaces are usually themselves algebraic varieties with a very rich geometry and topology, under current intensive research. Moduli space theory is indeed a vast and intricate topic, whose origins go back to Riemann and which have been behind several Fields Medals (like Mumford, Donaldson or Mirzakhani, just to name a few). Even their rigorous definition is not a trivial matter and, somehow contradicting the title, it will not be given in this talk. The aim is just to provide a general idea of what a moduli space is supposed to be and mainly focus on basic examples.

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