[geometry-ml:01319] Seminar at IPMU on 8/31 Ponge

[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)
http://ipmu.jp/

===========
Speaker: Raphael Ponge  (Seoul National University)

Time: Aug 31 (Wed) 15:30-17:00

Place: Seminar room A

Title: Noncommutative Geometry and the Hirzebruch-Riemann-Roch Formula

Abstract:

One aim of noncommutative geometry (in the sense of Alain Connes) is
to translate the classical tools of differential geometry in the
Hilbert space formalism of quantum mechanics. It is then expected that
noncommutative geometry will enable us to deal with a variety of
problems whose "noncommutative nature" prevents us from using the
usual tools of differential geometry (e.g., quantum space-time,
diffeomorphism-invariant geometry).

The Hirzebruch-Riemann-Roch formula gives a geometric expression for
the holomorphic Euler characteristic of a compact complex manifold in
terms of the integral of characteristic forms. It can be seen as a
special case of the local index formula of Atiyah-Singer, which
ultimately holds in the framework of noncommutative geometry.

In this talk, it is planned to report on on-going projects about using
noncommutative geometry to study the following geometric settings:

- Biholomorphism-invariant geometry of (strongly pseudoconvex) complex
domains, i.e., the geometry in the presence of  the action of an
arbitrary group of biholomorphisms of such a domain.

- Contactomorphism-invariant geometry of contact manifolds, i.e., the
geometry in the presence of the action of an arbitrary group of
contactomorphisms of a given contact manifold.

The main goal is to reformulate the Hirzebruch-Riemann-Roch formula
and the Atiyah-Singer index formula in these settings.

============
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/