U utorak, 18. veljače 2020., u 16 sati u predavaonici 104 (PMF-MO), u okviru Seminara za dinamičke sustave

Loïc Teyssier, Université de Strasbourg,

održat će predavanje pod naslovom:

"Non-algebraizable planar saddle-nodes".

Abstract:
We call "planar foliation" the local structure of the integral curves of a holomorphic vector field in the complex 2-plane. Far from stationary points the foliation is regular and can be (locally) straightened onto a product of discs. A generic singular foliation also admits a simple local structure, since it is linearizable by Poincaré's theorem. Geometrically speaking these properties are tantamount to saying that the typical foliation is the expression in a local chart of a global foliated compact complex surface. Is that a general fact? If not, how can one build examples of germs of a foliation which cannot arise as the localization of a global foliation? By considering saddle-node foliations (non-linear "irregular singular points") we are able to answer these questions. More specifically, we study in detail the process that brings a polynomial saddle-node foliation into its Loray normal form, and how doing so enlarges the field of definition of the foliation in a controlled way. As a result, normal forms whose field of definition has infinite transcendence degree over the rationals cannot be locally conjugate to an algebraic foliation.

Pozivaju se članovi seminara i svi zainteresirani da prisustvuju predavanju.

Lijep pozdrav,

Maja Resman