[geometry-ml:02408] MiniCourse"Poisson geometry from a symplectic perspective"David Matrinez Torres (PUC-RIo)

[yoshi ＠ math.chuo-u.ac.jp]

皆様；
重複して受け取られた際にはご容赦ください。

Mini-Cours 
by 
David Matrinez Torres (PUC-RIo) 

"Poisson geometry from a symplectic perspective"

のお知らせです。

PUC-Rio の David Martinez Torres 氏が４週間ほど日本に滞在されます。
この機会に Poisson 幾何、symplectic 構造に関するミニコースを
お願いいたしました。
かなり初等的な導入から、比較的 advanced なところまで解説していただく
予定です。

アブストラクトも含め、詳細は以下のURLをご覧ください。
http://www.math.chuo-u.ac.jp/seminar_D.M.Torres.htm

また、東京圏外からの参加を予定されている方で旅費の希望があれば、
若干の補助が可能ですので、
yoshi AT math.chuo-u.ac.jp
までご連絡ください。

三松　佳彦
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　　　　ENCOUNTERwithMATHEMATICS 番外編

               Mini-Course 
                   by 
      David Matrinez Torres (PUC-RIo) 

"Poisson geometry from a symplectic perspective"

7月18日(土) 16：00-17：00, 17：30-18：30 (中央大学理工学部6号館12階 
61225号室)
7月25日(土) 16：00-17：00, 17：30-18：30 (中央大学理工学部6号館12階 
61225号室)
8月 1日(土) 16：00-17：00, 17：30-18：30 (東京工業大学理学部本館の予定)

Abstract: Abstract:
       Poisson structures can be seen as generalizations of symplectic 
structures. This generalization is so flexible, that virtually no tool 
from symplectic geometry can be pushed to the Poisson setting. In this 
series of talks we aim at discussing up to which extent it is possible 
to select a class of Poisson structures for which some sort of `
symplectic approach’ is possible. 
       In more detail, we shall start with a brief introduction to 
Poisson geometry, stressing the many different approaches to the subject 
(classical mechanics, foliation theory, symplectic geometry). Next we 
shall describe a few fundamental problems in Poisson geometry and the 
difficulties to tackle them for arbitrary Poisson structures. 
       We continue introducing the class on integrable Poisson manifolds:
 roughly, these are Poisson manifolds dominated by symplectic manifolds 
(complete symplectic realizations). Equivalently, a Poisson structure 
defines a Lie algebroid structure (an infinite dimensional Lie algebra 
of `geometric nature'), and, integrable Poisson manifolds, they are 
those Poisson manifolds for which their associated Lie algebroid 
integrates into a Lie groupoid (the kind of structure which formalizes `
partial symmetries'). 
       We shall expend some time discussing how to recognize integrable 
Poisson manifolds (more generally, integrable algebroids), and, 
interestingly enough, we shall see how the integrability of a Poisson 
structure (of a general Lie algebroid) amounts to the smoothness of the 
leaf space of a foliation (on a Banach manifold). 
       After describing up to which extend the integrability assumption 
exerts control on the Poisson structure, we will see how imposing 
additional `compact type conditions' on symplectic integrations leads to 
a class of (rather rigid) Poisson manifolds with, to some extent, are a 
simultaneous generalization of compact symplectic manifolds, compact Lie 
algebras and compact/proper foliations. 


連絡先：中央大学・理工学部：三松　佳彦
TEL:03-3817-1749
E-MAIL:yoshiATmath.chuo-u.ac.jp