トピックス

2019年12月9日（月）立命館大学幾何学セミナー

2019.12.04 Wed up
<<立命館大学幾何学セミナー>>

日時：2019年12月9日（月） 16:30～17:30

タイトル：BV structures on moduli spaces of flat connections

講演者：Pavol Severa （University of Geneva）

アブストラクト：
Loops (or rather their homotopy classes) on an oriented surface form a Lie algebra, originally discovered by Goldman. The Lie bracket is given by a simple formula involving intersection points of two loops. This Lie algebra can be interpreted as the Poisson bracket on a moduli space of flat connections (given by the famous Atiyah-Bott symplectic form), if to each loop we assign the trace of the holonomy along the loop. Loops come also with another operation, a Lie cobracket discovered by Turaev, given by a very similar formula. I will explain what is the corresponding geometric structure on the moduli space. I will also try to explain why this structure is interesting and how it relates to the Kashiwara-Vergne problem in Lie theory. Based on a joint work in progress with Anton Alekseev, Florian Naef, and Jan Pulmann.

場所：立命館大学びわこ・くさつキャンパス（BKC）
　　　ウェストウィング 6階 談話会室

2019年11月11日（月）立命館大学幾何学セミナー

2019.10.30 Wed up
<<立命館大学幾何学セミナー>>

日時：        2019年11月11日（月） 16:30～17:30

タイトル：   
Lie algebras attached to a class of Clifford modules;
existence of lattices, their classification and automorphism groups

講演者：     古谷 賢朗 （東京理科大）

アブストラクト：
We consider a class of 2 step nilpotent Lie algebras which are  attached to a class of Clifford modules. We call them pseudo H-type algebras. They are a generalization of Heisenberg algebra. First we show the existence of integral lattices and explain how we classify them. Then we determine all the cases of their automorphism groups. Many properties of this algebra reduce to 49 basic cases by three periodicities, so called Bott periodicity. Finally I will  discuss about the uniqueness of the integral lattice.

場所：        立命館大学びわこ・くさつキャンパス（BKC）
　　　          ウェストウィング 6階 談話会室

International workshop on Geometry of Foliated Spaces

2019.10.24 Thu up
日時： ２０１９年１１月２９日（金）１３：３０～１２月１日（日）１２：００
会場： 立命館大学 びわこ・くさつキャンパス ウェストウィング6階 談話会室 キャンパスへのアクセス キャンパスマップ キャンパスマップ（pdfファイル）
住所： 滋賀県草津市野路東１－１－１
プログラム

１１月２９日（金）
13:30-14:20 Hitoshi Moriyoshi (Nagoya Univ.)
Geometry on the space of equi-centro-affine curves

14:40-15:30 Ramón Barral Lijó (Ritsumeikan Univ.)
Distinguishing colorings

15:50-16:40 Jesús Antonio Álvarez López  (Univ. of Santiago de Compostela)
Haefliger’s cohomology and tautness for matchbox manifolds

17:00-17:30 Subaru Nomoto (Ritsumeikan Univ.)
Some hierarchy in frames on curves on 4-dimensional Euclidean space

19:00- 懇親会 於 いさり火 庵


１１月３０日（土）
9:00-9:50 Ryuma Orita (Tokyo Metropolitan Univ.)
Rigid fibers of spinning tops

10:10-11:00 Olga Lukina  (Univ. of Vienna)
Cantor actions and Galois groups

11:20-12:10 Ramón Barral Lijó  (Ritsumeikan Univ.)
Breaking symmetry

14:30-15:20 Naoki Kato (Chukyo Univ.)
Turbulizations of transversely affine foliations of codimension two

15:40-16:30 Noboru Ito (Univ. of Tokyo)
A categorified Vassiliev skein relation on Khovanov homology

16:50-17:20 Norihisa Takahashi (Ritsumeikan Univ.)
Dehn twist presentations of hyperelliptic periodic maps


１２月１日（日）
9:00-9:50 Olga Lukina  (Univ. of Vienna)
Stabilizers of points for Cantor group actions

10:00-10:50 Tetsuya Abe (Ritsumeikan Univ.)
On annulus presentations of knots

11:10-12:00 Jesús Antonio Álvarez López  (Univ. of Santiago de Compostela)
A distributional trace formula for foliated flows


※ プログラムは変更されることがありますのであらかじめご了承ください。

連絡先：野澤 啓（立命館大理工）
E-mail：hnozawa（at）fc.ritsumei.ac.jp
Nov. 29: Program changed.
Oct. 24: Page created. First-announcement.
アブストラクト

Hitoshi Moriyoshi (Nagoya Univ.)

Title: Geometry on the space of equi-centro-affine curves

Abstract: A curve \(c\) on the Euclidean plane is called equi-centro-affine if it satisfies \(\mathrm{det} (c c’)=1\). The space of all equi-centro-affine curves on plane turns out to be a manifold of infinite dimension, which admits an interesting action by the group of orientation-preserving diffeomorphisms on unit circle. In this talk, we exhibit invariant pre-symplectic forms on the infinite-dimensional manifold and momentum maps related to those forms, which are also involved with the celebrated Gelfand-Fuchs \(2\)-cocycle.


Ramón Barral Lijó (Ritsumeikan Univ.)

Title: Distinguishing colorings

Abstract: We will introduce the concepts or distinguishing and limit distinguishing colorings for graphs, as well as the corresponding indices. We will also present known results and bounds for these indices for different families of graphs.


Jesús Antonio Álvarez López  (Univ. of Santiago de Compostela)

Title: Haefliger’s cohomology and tautness for matchbox manifolds

Abstract: (joint work with Steven Hurder and Hiraku Nozawa) For a compact foliated space \(\mathfrak M\) of dimension \(p\), we introduce a cochain complex which combines the de~Rham complex along the leaves and the Alexander-Spanier complex in the transverse direction. This complex also has a filtration by differential spaces, giving rise to a version of the Leray spectral sequence \((E_k^{u,v},d_k)\) for \(\mathfrak M\). The part \(E_2^{\cdot,p}\) is a version of the Haefliger cohomology for \(\mathfrak M\), which can be used to characterize a version of tautness like in the case of foliations on compact manifolds. In particular, all matchbox manifolds are taut in our sense.


Subaru Nomoto (Ritsumeikan Univ.)

Title: Some hierarchy in frames on curves on 4-dimensional Euclidean space

Abstract: Bishop introduced a frame on space curves different from the well known Frenet frame. It is characteristic that any regular space curve admit this frame. For curves on R^4, there are four different type of Bishop type frames including the Frenet frame and the Bishop frame. In this talk, we discuss the relation between these four types of frames from the viewpoints of geometric structures on normal bundle f curves and ordinary differential equations.


Ryuma Orita (Tokyo Metropolitan Univ.)

Title: Rigid fibers of spinning tops

Abstract: In the talk, we deal with fibers of classical Liouville integrable systems containing the Lagrangian top and the Kovalevskaya top. Especially, we find a non-displaceable fiber for each of them. To prove these results, we use the notion of superheaviness introduced by Entov and Polterovich. This is a joint work with Morimichi Kawasaki (RIMS).


Olga Lukina  (Univ. of Vienna)

Title: Cantor actions and Galois groups

Abstract: In this talk, we consider applications of dynamical invariants for Cantor group actions in Number theory, namely for the study of a certain type of representations of absolute Galois groups of number and function fields.


Ramón Barral Lijó (Ritsumeikan Univ.)

Title: Breaking symmetry

Abstract: We will contextualize the previous talk in the setting of the Gromov space of graphs, and will present some applications to other areas of mathematics.


Naoki Kato (Chukyo Univ.)

Title: Turbulizations of transversely affine foliations of codimension two

Abstract: In 1980, Seke gave a condition for turbulized foliations of codimension one transversely affine foliations to have transverse affine structures again. Recently, Mitsumatsu and Vogt defined the notion of turbulizations for higher codimensional foliations. In this talk, we give a condition for turbulized foliations of codimension two transversely affine foliations to have transverse affine structures again.


Noboru Ito (Univ. of Tokyo)

Title: A categorified Vassiliev skein relation on Khovanov homology

Abstract: This is a joint work with Jun Yoshida (The University of Tokyo). In this talk, we define a chain map that categorifies the operation “crossing change” on Khovanov homology using a canonical short exact sequence of a mapping cone at each crossing of a link diagram. The chain map is invariant under moves of singular knots. By the setting, taking graded Euler characteristics, a Vassiliev skein relation for a Jones polynomial is recovered.


Norihisa Takahashi  (Ritsumeikan Univ.)

Title: Dehn twist presentations of hyperelliptic periodic maps

Abstract: Ishizaka classified up to conjugation hyperelliptic periodic diffeomorphisms of surfaces and gave Dehn twist presentations in terms of Humphries generators. In this talk, we will give an explicit decomposition of surfaces into pentagonal fundamental domains of hyperelliptic periodic diffeomorphisms. As an application, we obtain the Dehn twist presentations of hyperelliptic periodic mapping classes, which are closely related to the ones obtained by Ishizaka.


Olga Lukina  (Univ. of Vienna)

Title: Stabilizers of points for Cantor group actions

Abstract: We study properties of stabilizers of points for Cantor group actions, such as the number of distinct stabilizers of points without holonomy, and the genericity of points with non-trivial holonomy in a measure-theoretical sense. We then apply our results to study the properties of invariant random subgroups, defined by such action. Joint work with Maik Groeger.


Tetsuya Abe (Ritsumeikan Univ.)

Title: On annulus presentations of knots

Abstract: In 2013, Jong, Omae, Takeuchi and I introduced the notion of annulus presentations of knots. In this talk, we discuss the following topics:

1. Why we are interested in annulus presentations of knots.
2. An obstruction to knots admitting annulus presentations in terms of the Jones polynomial.
3. Table of knots which admit annulus presentations up to 8 crossings.

This is joint work with Keiji Tagami. Note that Gen Suzuki (who is a student of Ritsumeikan University) partially made the table of knots which admit annulus presentations up to 8 crossings.


Jesús Antonio Álvarez López  (Univ. of Santiago de Compostela)

Title: A distributional trace formula for foliated flows

Abstract: Let \(\mathcal F\) be a smooth codimension one foliation on a compact manifold \(M\). A flow \(\phi^t\) on \(M\) is said to be foliated if it maps leaves to leaves. If moreover the closed orbits and preserved leaves are simple, then there are finitely many preserved leaves, which are compact, forming a compact subset \(M^0\), and a precise description of the transverse structure of \(\mathcal F\) can be given. A version of the reduced leafwise cohomology, \(\overline{H}I(\mathcal F)\), is defined by using distributional leafwise differential forms conormal to \(M^0\). The talk will be about our progress to define distributional traces of the induced action of \(\phi^t\) on \(\overline{H}^rI(\mathcal F)\), for every degree \(r\), and to prove a corresponding Lefschetz trace formula involving the closed orbits and leaves preserved by \(\phi^t\). The formula also involves a distributional version of the \(\eta\)-invariant of \(M^0\), which might be zero. This kind of distributional trace formula was conjectured by Christopher Deninger, and it was proved by the first two authors when \(M^0=\emptyset\).
End of this page.

2019年10月15日(火) ワークショップ

2019.09.26 Thu up
”Ritsumeikan One Day Workshop on Probability and Statistics”
 
日時：2019年10月15日(火） 11：00～18：00
場所：立命館大学びわこくさつキャンパス　ウエストウイング6階　談話会室
詳細はこちら

2019年8月2日（金）立命館大学数理工学セミナー

2019.07.20 Sat up
<<立命館大学数理工学セミナー>>

日時：      2019年8月2日（金） 16:00～18:00

タイトル： 機械学習への数理科学的アプローチ

講演者：  池田 和司 （奈良先端科学技術大学院大学）

アブストラクト：
近年の人工知能ブームの基礎は機械学習である．機械学習にはさまざまなアルゴリズムがあるが，それらは必ずしも理論的に導出されたものではない．数理科学はこのようなヒューリスティクスに対し，理論的な裏付けを与えることができる．本セミナーでは，発表者がこれまでに研究してきたサポートベクトルマシンの理論，オンライン学習の理論，深層学習の理論などを紹介する．

場所：     立命館大学びわこ・くさつキャンパス（BKC）
　　　       ウェストウィング 6階 談話会室

2019年7月17日（水）・24日（水）　集中講義

2019.07.17 Wed up
立命館大学数理科学科集中講義

7月17日(水)，7月24日（水）に数理科学科集中講義を開講いたします．
量子ウォークに関する初学者向け連続講義となります．
奮ってご参加下さい．

日時：2019/7/17(水) 13:00 – 16:10 
 2019/7/24(水) 13:00 – 16:10 
場所：立命館大学びわこ・くさつキャンパス
 ウェストウィング7階数学第4研究室
講師：小栗栖 修 氏
タイトル：量子ウォーク
内容： 第1回 7/17(水) 13:00 – 14:30 量子ウォークの定義と基本的な性質
 第2回 7/17(水) 14:40 – 16:10 量子ウォークの周期性の問題
 第3回 7/24(水) 13:00 – 14:30 量子ウォークと量子探索アルゴリズム
 第4回 7/24(水) 14:30 – 16:10 量子トンネルに係る話題
 
懇親会：7月17日の晩に懇親会を開催いたします．
 ご参加いただける方は広田（hirota@fc.ritsumei.ac.jp）まで
 ご連絡くださいますようお願い申し上げます．
 

2019年7月29日（月）立命館大学幾何学セミナー

2019.07.08 Mon up
<<立命館大学幾何学セミナー>>

日時：        2019年7月29日（月） 17:30～19:00

タイトル：    Petrov Module for a Family of Generalized Liénard Integrable Systems

講演者：     Lucile Mégret （Sorbonne Université）

アブストラクト：
PDFファイルをご覧ください．

場所：        立命館大学びわこ・くさつキャンパス（BKC）
　　　          ウェストウィング 6階 談話会室

2019年6月20日（木）立命館大学幾何学セミナー

2019.06.06 Thu up
<<立命館大学幾何学セミナー>>

日時：        2019年6月20日（木） 10:40～12:10

タイトル：    光の分散関係の構造と物理現象

講演者：     澤田 桂 （理化学研究所 放射光科学研究センター）

アブストラクト：
光などの波動において、周波数と波数ベクトルとの関係式を分散関係と呼ぶ。分散関係は曲面で表され、その形状は、波動が伝わる媒質の構造や対称性によって異なる。例えば等方的な媒質では２次曲面になり、異方的な媒質では特異点をもつ４次曲面にもなりうる。本講演では、光の分散関係に着目し、その曲面の構造がもたらす様々な光学現象を考察する。日常でも目にする屈折などの基本的な現象の説明から始め、分散関係の曲面が特異点をもつ場合の光の振舞いとその理論的背景を解説する。具体例として、特異性を反映したトポロジカルな性質によるエッジ状態や、円錐状に光が伝わる円錐屈折などについて、実験結果も交えつつ述べる。

場所：        立命館大学びわこ・くさつキャンパス（BKC）
　　　          ウェストウィング 6階 談話会室

2019年5月25日(土)・26日(日) 研究集会「幾何学と力学とその応用」

2019.05.05 Sun up
研究集会「幾何学と力学とその応用」
(Geometry, Mechanics, and their Applications）

日時：     2019年5月25日（土）10:00～26日（日）17:00

場所：     立命館大学びわこ・くさつキャンパス
             ウェストウィング 6階談話会室

世話人： 上野嘉夫（京都薬科大学），佐藤寛之（京都大学），多羅間大輔（立命館大学），中村佳正（京都大学），吉村浩明（早稲田大学）

連絡先： 多羅間大輔 （e-mail: dtarama[at]fc.ritsumei.ac.jp）

プログラム（PDFファイルをご覧ください）

2019年9月1日(日)～7日(土)　ワークショップ

2019.04.05 Fri up
The Fifth Japan-China Geometry Conference 

Dates: September 1–September 7, 2019
Conference Venue: Ritsumeikan University,  Biwako-Kusatsu Campus (BKC), West-Wing
 
Organizers: 
 
Scientific Committee:
       Akito Futaki (Tsinghua University)
       Anmin Li (Sichuan University)
       Toshiki Mabuchi (Osaka University)
       Yoshihiro Ohnita (Osaka City University)
       Gang Tian (Peking University)
       Weiping Zhang (Chern Institute of Mathematics)
 
Organizing Committee:
       Qing-Ming Cheng (Fukuoka University)
       Qing Ding (Fudan University)
       Ryushi Goto (Osaka University)
       Ryoichi Kobayashi (Nagoya University)
       Haizhong Li (Tsinghua University)
       Jiayu Li (University of Science and Technology of China)
       Reiko Miyaoka (Tohoku University)
       Hitoshi Moriyoshi (Nagoya University)
       Takashi Shioya (Tohoku University)
       Zizhou Tang (Chern Institute of Mathematics)
       Changping Wang (Fujian Normal University)
 
Local Organizers:
       Hiroyuki Osaka (Ritsumeikan University)
       Toshikazu Natsume (Ritsumeikan University)
  
Invited Speakers:
       Daguang Chen (Tsinghua University)
　　Fuquan Fang (Capital Normal University)
       Atsushi Fujioka (Kansai University)
       Pengfei Guan (McGill University)
       Xiaoli Han (Tsinghua University)
       Shohei Honda (Tohoku University)
       Rongli Huang (Guangxi Normal University) 
       Masashi Ishida (Tohoku University)
       Xiaoshang Jin (Peking University)
       Haizhong Li (Tsinghua University)
       Toshiki Mabuchi (Osaka University)
       Shin-ichi Ohta  (Osaka University)
       Kaoru Ono (Kyoto University)
       Chao Qian (Beijing Institute of Technology)
       Li Sheng (Sichuan University)  
       Gang Tian (Peking University)
       Peng Wang  (Fujian Normal University)
       Yong Wei (University of Science and Technology of  China and Australian National University)
       Hongwei Xu (Zhejiang University)
       Takao Yamaguchi (Kyoto University)
       Xi Zhang (University of Science and Technology of China)
       
For information:
　　Q.-M. Cheng  (cheng@fukuoka-u.ac.jp) 
       R. Miyaoka (r-miyaok@m.tohoku.ac.jp)
       H. Moriyoshi (moriyosi@math.nagoya-u.ac.jp)

Supported by :
　　JSPS Grants (Q.-M. Cheng, R. Goto, R. Miyaoka, H. Moriyoshi, T. Shioya), and
　　Department of Mathematical Science, Ritsumeikan University

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