Contents/conteúdo

Mathematics Department Técnico Técnico

Informal Geometry Seminar  RSS

Sessions

18/02/2014, 11:15 — 12:15 — Room P3.10, Mathematics Building
Alfonso Zamora, Instituto Superior Tecnico

GIT and symplectic stability(I)

Geometric Invariant Theory (GIT) is a powerful tool to study quotients of algebraic varieties by the action of Lie groups, related to symplectic quotients by the Kempf-Ness theorem. From both points of view a notion of stability for the orbits of the group action plays a prominent role.

In the lectures we will give the basic notions and ideas behind GIT stability, symplectic stability and the Kempf-Ness theorem.

We will pay special attention to the unstable orbits for which one can finds a "maximal way to destabilize" them. This idea can be seen from both the algebraic and the symplectic point of view and we will show this coincidence. All the treatment will be done through three (basic but very illustrative) examples: the obtention of the projective space as a quotient, the moduli space of configurations of n points in the projective line (related to the moduli space of polygons) and the obtention of the grassmanian as a quotient.


The Informal Geometry Seminar, as its name says, is an informal seminar for graduate students and postdocs at IST to share their ideas with each other and a good place to ask simple questions without any pressure.