|Speaker:||Isaia Nisoli (U Pisa)|
|Title:||Index and residue theorems in holomorphic dynamics, an overview and some recent developments|
|Date (JST):||Fri, May 15, 2009, 15:30 - 17:00|
|Place:||Seminar Room at IPMU Prefab. B|
Index theorems have a prominent role in the study of both continuous and discrete holomorphic dynamics. They are used to prove the existence of topological obstructions to global integrability (Baum-Bott), to prove the existence of complex separatrix in complex dimension 2 (Camacho-Sad), to extend the Leau-Fatou flower theorem to higher dimension (Abate).
In the first part of my talk I will give account of these results, giving an overview of the the applications of index and residue theorems in dynamics, while in the second, more technical part, I will present some recent results, dealing with the existence of the local variation action, a partial holomorphic connection which gives rise to an extension of the variation index theorem by Lehmann, Khanedani and Suwa."