## 3 événements

• Géométrie complexe

### Vendredi 13 avril 09:00-10:00 - Ruadhai Dervan - Cambridge / Ecole Polytechnique

Extremal metrics on fibrations

Résumé : I will discuss a construction of certain canonical Kähler metrics on fibred complex manifolds, which extends work of Fine. The main new idea is to exploit the Kähler geometry of maps between complex manifolds. This is joint work with Lars Sektnan.

• Systèmes Dynamiques

### Vendredi 13 avril 10:30-11:30 - Valente Ramirez - Cornell University

The spectra of singularities of quadratic vector fields

Résumé : Consider a polynomial vector field of degree $n \geq 2$ on $C^2$. In the generic case, it has $n^2$ isolated singularities, and the holomorphic foliation it defines on $P^2$ has an invariant line at infinity with $n+1$ singular points.

Lieu : salle 207, bat 1R2

• Géométrie complexe

### Vendredi 13 avril 10:30-11:30 - Ruadhai Dervan - Cambridge/Ecole Polytechnique

Stable maps in higher dimensions

Résumé : Kontsevich’s version of Gromov-Witten theory rests on the
notion of a "stable map" from a curve to a variety. I will discuss a
notion of stability for maps between arbitrary varieties, which
generalises Kontsevich’s definition when the domain is a curve and
Tian-Donaldson’s definition of K-stability when the target is a point. I will discuss some examples, and also an analogue of the Yau-Tian-Donaldson conjecture in this setting, which relates stability to the existence of certain canonical Kähler metrics. This is joint
work with Julius Ross.