MS Seminar (Mathematics - String Theory)

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
Abstract: 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."