[geometry-ml:05655] 奈良幾何表現論セミナーのご案内

[matsuzawa]

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松澤淳一
〒630-8506 奈良市北魚屋西町
奈良女子大学　岡数学研究所　
Phone: 0742-20-3361 (研究室)
FAX: 0742-20-3367 (事務室）
matsuzawa ＠ cc.nara-wu.ac.jp


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奈良幾何表現論セミナー

日時：  2024年5月9日（木）10：30−17：30
場所：  奈良女子大学理学系B棟４階 第3セミナー室B1403

 10：30−11：30   Toshihisa Kubo (Ryukoku University)
On the projectively covariant differential operators on real projective spaces

 13：30−14：30   Dennis The (UiT The Arctic University of Norway)
On 4D split-conformal structures with G2-symmetric twistor distribution

 15：00−16：00   Daisuke Tarama (Ritsumei University)
Geodesic flows associated to statistical transformation models

 16：30−17：30   Tohru Morimoto (Oka Mathematical Institute)
Classification of the symbols of pseudo-subriemannian contact structures

松澤淳一 （奈良女子大学，岡数学研究所）
森本 徹 （奈良女子大学，岡数学研究所）


[Abstracts]

Speaker: Toshihisa Kubo
Title：On the projectively covariant differential operators on real projective spaces
 Abstract：Construction and classification of covariant differential operators are 
classical problems in parabolic geometry. In 1976, Fegan accomplished to classify 
and construct conformally covariant differential operators of first order. Since then, 
the results of Fegan have been generalized by Cap-Slovak-Soucek, Slovak-Soucek, 
Ørsted, Koranyi-Reimann, among others. The first order case is now settled.
  Higher order case is in contrast still a work in progress. 
In 2015, Kobayashi-Ørsted-Somberg-Soucek obtained, among many other things, 
explicit formulas of differential symmetry breaking operators and conformally covariant 
differential operators on a natural line bundle over a conformal sphere. In this talk, we 
shall classify and construct projectvely covariant differential operators on real projective spaces.
 If time permits, we would also like to discuss such operators in a symmetry breaking setting. 
This talk is partially based on joint work with Bent Ørsted.

Speaker: Dennis The (UiT The Arctic University of Norway)
Title: On 4D split-conformal structures with G2-symmetric twistor distribution
Abstract: In their 2013 article, An & Nurowski considered two surfaces rolling on each other 
without twisting or slipping, and defined a twistor distribution (on the space of all real totally 
null self-dual 2-planes) for the associated 4D split-signature conformal structure.  
If this split-conformal structure is not anti-self dual, then the twistor distribution is a (2,3,5)-distribution, 
and An-Nurowski identified interesting rolling examples where it achieves maximal, i.e. G2, symmetry. 
 Relaxing the rolling assumption, a similar construction can be made for any 4D split-conformal structure, 
and my talk will discuss a broader classification of examples where such exceptional symmetry for the 
twistor distribution is achieved.  (Joint work with Pawel Nurowski & Katja Sagerschnig.)

 Speaker: Daisuke Tarama
Title: Geodesic flows associated to statistical transformation models
Abstract:A statistical transformation model consists of a smooth data manifold, on which 
a Lie group smoothly acts, and a family of probability density functions on the data manifold 
parametrized by elements in the Lie group.For such a statistical transformation model, 
the Fisher–Rao (semi-definite) metric and the Amari–Chentsov cubic tensor are defined 
on the Lie group and their information geometry is of much interest.
In this talk, the general framework of statistical transformation models is explained.Then, 
the left-invariant geodesic flows associated with the Fisher–Rao metric  on Lie groups are
 considered for two specific models.
The geometric properties of the geodesic flows are studied from the viewpoint of geometric 
mechanics and subriemannian geometry.
The talk includes some of the collaborations with Jean-Pierre Françoise (Sorbonne Université).

 Speaker: Tohru Morimoto (Oka Mathematical Institute)
Title: Classification of the symbols of pseudo-subriemannian contact structures
Abstract: In this talk I will give a classification of the symbols, that is, first order approximations, 
of pseudo-riemannian contact structures.
This is an interesting problem of linear algebras to classify the pairs $(\frak h, \sigma )$,
 where $\frak h$ is a Heisenberg two step graded Lie algebra $\frak h_{-1} \oplus  \frak h_{-2} $
and $\sigma $ is a symmetric bilinear form on $\frak h_{-1}$ non-degenerate but not necessarily
 positive definite.It is a preliminary step to understanding the variety of pseudo-subriemannian structures.

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