[geometry-ml:01589] Seminar at Kavli IPMU on 2012 Nov 6 Lorscheid

[Satoshi Kondo]

Dear colleagues:

There will be a seminar as follows at Kavli IPMU
(Kavli Institute for the Physics and Mathematics of
the Universe).

Regards,

Satoshi Kondo (Kavli IPMU)
http://www.ipmu.jp/
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Speaker:	 Oliver Lorscheid (IMPA)

Title:	 A problem of Jacques Tits and Chevalley groups over F1

Date:	Tue, Nov 06, 2012, 13:15 - 14:45

Place:	Seminar Room A

Abstract:	 One of the main motivations of F1-geometry is to explain
the analogy between Chevalley groups over finite fields and the
combinatorial geometry of their Weyl groups. The idea to explain the
combinatorial part as a geometry over an elusive field, which is
nowadays called F1, "the field with one element", goes back to a paper
of Jacques Tits from 1956.

This idea entered the flourishing area of F1-geometry as the formula
G(F1)=W, and many authors contributed to it. However, the viewpoint
that the F1-rational points of a Chevalley group G should equal its
Weyl group W faces a certain functorial problem.

After giving a general introduction into the problem and the ideas of
F1-geometry, I will explain how the framework of blueprints provides a
natural solution to the problem. In particular, I will introduce the
so-called Tits-category, which contains models of Chevalley groups
over F1 that yield the Weyl groups in a functorial way.
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You can check the location from
http://www.ipmu.jp/access-0
The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/