ICTP Math Associates Seminar (Zoom Meeting) - Thursday 18 June, at 14:00 (Carolina Araujo)

[ICTP/math - Mabilo Koutou]

ICTP MATH ASSOCIATES SEMINAR


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Date: Thursday 18th June at 14:00 (CET)


Speaker: Carolina Araujo (IMPA)
Webpage: https://impa.br/page-pessoas/carolina-araujo/


Title: Symmetries in Algebraic Geometry and the Cremona Group


Abstract: In this talk I will discuss symmetries of complex algebraic
varieties. When studying a projective variety $X$, one usually wants to
understand its symmetries. Conversely, the structure of the group of
automorphisms of $X$ encodes relevant geometric properties of $X$. After
describing some examples of automorphism groups of projective varieties, I
will discuss why the notion of automorphism is too rigid in the scope of
birational geometry. We are then led to consider another class of
symmetries of $X$, its birational self-maps. The group of birational
self-maps of the projective space $\mathbb{P}^n$ is known as the Cremona
group in dimension $n$. Describing the structure of the Cremona group is a
major problem in algebraic geometry. While the theory is well developed in
dimension $2$, little is known in dimension $\geq 3$, and a natural
problem is to construct special subgroups of the Cremona group. I will
present a recent work with Alessio Corti and Alex Massarenti, where we
investigate subgroups of the Cremona group consisting of symmetries
preserving some special meromorphic volume forms.