[geometry-ml:00856] Seminar at IPMU on 2009/5/15

[Satoshi Kondo]

Dear colleagues:

We announce the following seminar at IPMU
(the Institute for the Physics and Mathematics of the Universe).

Regards,

Satoshi Kondo (IPMU)

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Speaker: 	 Tatsuo Suwa (Hokkaido University)
Title: 	Residues of Chern classes
Date: 	May 15, 2009, 13:30 - 15:00
Place: 	Seminar Room at IPMU Prefab. B
Abstract: The talk is concerned with localization of characteristic classes of
vector bundles (or sheaves) and the associated residues.
If we have some geometric object, certain characteristic classes are
localized at the
singular set of the object, and we have “Residue Theorems”, the
Poincar´e-Hopf Index
Theorem for vector fields being a model example.
The localization is done in the framework of the Chern-Weil theory
adapted to the
Cech-de Rham cohomology. Here I mainly talk about the localization of
Chern classes
of complex vector bundles on manifolds, or more generally singular
varieties, by non-
vanishing sections or frames. A direct comparison of the above
viewpoint with the ob-
struction theoretic definition of Chern classes leads to many
interesting results. The
importance of the Thom class in this framework will also be emphasized.

In the first part, I start with the basic case of the order of a zero
of a holomorphic
function of one variable. This integer, which has various interesting
interpretations, such
as analytic, algebraic and topological ones, can be viewed as a
residue of the first Chern
class of a line bundle. Then I talk about the residues at an isolated
singular point in the
case of general vector bundles.

In the second part, I will describe the residues in a more general
setting where the
singular set may be non-isolated and the base space may also be
singular. Then I explain
how this can be applied to construct an analytic intersection theory
on singular varieties.
I also mention the case of Atiyah classes if time permits.
-----------------------------------------------------------------------------------
Speaker: 	 Isaia Nisoli (U Pisa)
Title: 	Index and residue theorems in holomorphic dynamics, an
overview and some recent
Date: 	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."
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You can check the location from
http://www.ipmu.jp/access/img/KashiwaCampusMap.png

The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/?mode=seminar_recent