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### 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>>

タイトル：

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

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.

ウェストウィング 6階 談話会室

### 立命館大学幾何学セミナー

2019.10.24 Thu up
 日時： 12月2日（月） 16:20-17:50 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 講演者： Jesús Antonio Álvarez López氏（サンティアゴ・デ・コンポステラ大学） タイトル： Topological Molino’s theory アブストラクト： (joint work with Ramón Barral Lijó and Manuel Moreira Galicia) Molino’s description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are dense. In particular, a structural local group is associated to such a foliated space. As applications, we obtain a partial generalization of results by Carrière and Breuillard-Gelander, relating the structural local group to the growth of the leaves, and a description of foliated homogeneous spaces.

### 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

14:30-15:20 Ramón Barral Lijó (Ritsumeikan Univ.)
Distinguishing colorings

15:40-16:30 Jesús Antonio Álvarez López  (Univ. of Santiago de Compostela)
Haefliger’s cohomology and tautness for matchbox manifolds

16:40-17:40 TBA

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

10:00-10:50 Olga Lukina  (Univ. of Vienna)
Cantor actions and Galois groups

11:10-12:00 Ramón Barral Lijó  (Ritsumeikan Univ.)
Breaking symmetry

14:00-14:50 Naoki Kato (Chukyo Univ.)
Turbulizations of transversely affine foliations of codimension two

15:00-15:50 Noboru Ito (Univ. of Tokyo)
A categorified Vassiliev skein relation on Khovanov homology

16:10-17:40 TBA

19:00- JR草津駅近くの会場における懇親会

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。

E-mail：hnozawa（at）fc.ritsumei.ac.jp

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.

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.

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 $$M^0=\emptyset$$.

### 立命館大学幾何学セミナー

2019.10.23 Wed up
 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 講演者： Olga Lukina氏（ウィーン大学）

### Talk 1

 日時： 11月25日（月） 16:20-17:50 タイトル： Introduction to group actions on Cantor sets アブストラクト： In this talk, we consider basic tools and properties which we use in the subsequent talks to study minimal equicontinuous group actions on Cantor sets. The tools include chains of finite index subgroups. An important property is the local quasi-analyticity of an action, introduced by Alvarez Lopez and Candel. We illustrate the concepts and methods using examples.

### Talk 2

 日時： 11月28日（木） 10:40-12:10 タイトル： Invariants of Cantor group actions アブストラクト： In this talk, we consider two direct limit invariants which can be associated to a Cantor group action, introduced in a recent joint work with Steve Hurder, and the corresponding classification of Cantor group actions. It is recommended that the participants attend Talk 1 as a preparation for this talk.

### Math-Fi seminar on 10 Oct.

2019.10.07 Mon up
• Date: 10 Oct. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:30-18:00
• Speaker: Dan Crisan (Imperial College London)
• Title: second lecture

### Math-Fi seminar on 3 Oct.

2019.09.30 Mon up
• Date: 3 Oct. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:30-18:00
• Speaker: Dan Crisan (Imperial College London)
• Title: Modelling multi-period carbon markets using singular forward backward SDEs
• Abstract:
I will introduce a model the evolution of emissions and the price of emissions allowances in a carbon market such as the European Union Emissions Trading System (EU ETSP). The model accounts for multiple trading periods (and phases) and multiple times at which compliance can occur. At the end of each trading period, the participating firms must surrender allowances for the emissions made during that period, but any excess allowances can be used for compliance in the following periods. We show that the multi-period allowance pricing problem is well-posed for various mechanisms linking the trading periods (such as banking, borrowing and withdrawals). The results are based on the analysis of a forward-backward stochastic differential equation with the following special characteristics: i. the forward and backward components are coupled,  ii. the final condition is singular and iii. the forward component of the model is degenerate. I will also introduce an infinite period model, that is, a model for carbon market with a sequence of compliance times and no end date. I will show that, under appropriate conditions, the value function for the multi-period pricing problem converges, as the number of periods increases, to a value function for this infinite period model. This is joint work with Jean-Francois Chassagneux (Paris Diderot) and Hinesh Chotai (Citybank).

### 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”

### Math-Fi seminar on 12 Sep.

2019.09.09 Mon up
• Date: 12 Sep. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:30-18:00
• Speaker: José Manuel Corcuera (Universitat de Barcelona)
• Title: Contingent Convertibles (final lecture)

### Math-Fi seminar on 29 Aug.

2019.08.05 Mon up
• Date: 29 Aug. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:00-18:00
• Speaker: Wei Zhu/Maoqi Hu (University of Liverpool)
• Title: Introduction to Ruin Theory (final lecture)
• Abstract:
Risk theory in general and ruin probabilities in particular are traditionally considered as part of insurance mathematics, and has been an active area of research from the days of Lundberg all the way up to today. One of the central topics in the risk theory literature is deriving the probability of ruin in the collective risk model. The classical risk model and renewal risk models will be focused in this course, where the claim number processes are assumed to be Poisson counting processes and any general renewal counting processes, respectively.

The first part of this course is about the classical risk model. Different approaches to derive the ruin probability will be shown and explained. The natural extension of the classical risk model leads to the renewal risk model. Very general assumptions on interarrival times are possible for the renewal risk model, which includes the classical risk model, Erlang risk model and fractional Poisson risk model. A new family of differential operators are defined in order to construct the fractional integro-differential equations for ruin probabilities in such renewal risk models. Through the characteristic equation approach, specific fractional differential equations for the ruin probabilities can be solved explicitly, allowing for the analysis of the ruin probabilities

### Math-Fi seminar on 22 Aug.

2019.08.05 Mon up
• Date: 22 Aug. (Thu.)
• Place: W.W. 6th-floor, Colloquium Room
• Time: 16:00-18:00
• Speaker: Wei Zhu/Maoqi Hu (University of Liverpool)
• Title: Some Aspects about Life Insurance and Life Expectancy in China (second lecture)
• Abstract:
​Life insurance has undergone enormous change in the last two to three decades. Given the changes occurring in the interconnected worlds of finance and life insurance, we believe that this is a good time to recast the mathematics of life contingent risk to be better adapted to the products, science and technology that are relevant to current and future actuaries. Pension, a part of the life insurance, is an importance insurance in our life. However, most countries face the challenge in pension. Population aging and life expectancy both of these will influence the pension system. The course will first introduce the background and give some basial theories about life insurance and pension. Then the course will discuss the influence factors of life expectancy and also use Spatial Statistical tools to assess mortality differences in China.