立命館大学数理科学科

セミナー

Math-Fi seminar on 17 Jan.

2020.01.14 Tue up

Date: 17 Jan. (Fri.)
Place: W.W. 6th-floor, Colloquium Room
Time: 16:30-18:40

First Speaker: Yushi Hamaguchi (Kyoto University)
Time: 16:30-17:30
Title: Time-inconsistent consumption-investment problems in incomplete markets
Abstract:

　投資家の時間選好を表す割引関数が古典的な指数割引関数でない場合、Bellmanの最適性原理が成立せず、効用最大化問題は時間非整合となることが知られている。つまり、現時点で見たときの将来の利得に関する最適戦略が、後の時点で見ると最適戦略とはならない。近年、このような時間非整合的な最適化問題が、確率制御理論、数理ファイナンス、経済学などで注目されている。本講演では、非マルコフかつ非完備マーケットの設定において、一般の割引関数の下での投資家の消費・投資戦略に関する効用最大化問題を考える。この問題において、時間非整合的な「最適戦略」に取って代わる時間整合的な解概念である「ナッシュ均衡戦略」の定義を紹介し、そのFBSDEを用いた特徴づけ、および時間整合的な効用最大化問題との対応について得られた結果を説明する。

Second Speaker: Yuki Ueda (Hokkaido University)
Time: 17:40-18:40
Title: Introduction to free probability theory and infinitely divisible distributions
Abstract:

　自由群に付随した非可換量の考察から生まれた自由確率論は、古典確率論との関連深い結果を多く含む。本講演では、自由確率論の初歩から始め、古典確率論と特に関連があるものの一つである、分布の自由無限分解可能性について解説する。

2020年1月20日（月）立命館大学幾何学セミナー

2020.01.07 Tue up

<<立命館大学幾何学セミナー>>

日時：2020年1月20日（月） 16:30～18:00

タイトル：数学使いの新たな道　―「データサイエンティスト」とは―

講演者：板井　光輝（(株)日立システムズ）

アブストラクト（予定）：
本セミナーでは、データサイエンティストの役割・職種とデータサイエンス業務で必要とされるスキルを説明します。
また、多様体論等の幾何学分野を活かした“AI技法”と実務適用における重要な数学のキーワードや、データサイエンスの事例も紹介します。

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

Math-Fi seminar on 9 Jan.

2020.01.07 Tue up

Date: 9 Jan. (Thu.)
Place: W.W. 6th-floor, Colloquium Room
Time: 16:00-19:00

First Speaker: Katsushi Nakajima (Ritsumeikan Asia Pacific University)
Time: 16:00-17:30
Title: TBA

Second Speaker: Koya Sakakibara (Kyoto University)
Time: 17:30-19:00
Title: Numerical analysis of interface problem
Abstract:

The interface appears in several problems, such as fluid dynamics between two different liquids. To study its evolution and dynamics forms the basis of the research in natural science. Although there are several mathematical studies for interfacial phenomena, they are, in general, so difficult, and numerical study becomes an essential tool in this field.

In this talk, I will talk about the numerical analysis of interface problem, and especially consider two issues: The Hele-Shaw problem and grain boundary. The Hele-Shaw problem describes the motion of viscous fluid in a quasi-two-dimensional space, which started from a short paper by Henry Selby Hele-Shaw (1854–1941). It is now recognized as a basic mathematical model to study the fingering phenomena (also known as the Saffman–Taylor instability), and several researchers have studied this problem; however, there are still several open questions. A problem on the grain boundary appears in the field of material science. A grain boundary is an interface between two grains, or crystallites, in a polycrystalline material. It is the two-dimensional defect in the crystal structure. The study of grain boundaries and their effects on the mechanical, electrical, and other properties of materials forms an essential topic in material science. My study aims to understand the mechanism of grain boundaries from mathematical and numerical points of view.

In the first half of this talk, I will explain this problem and construct some efficient numerical scheme based on the method of fundamental solutions and the asymptotic uniform distribution method. I will also briefly survey the geometric numerical integration, which aims to construct a numerical scheme which inherits properties of the original problem in some discrete sense. In the second half of this talk, I will move on to the problem on grain boundaries and consider manifold-valued total variation flows. I will introduce spatially discretized total variation flow and construct a numerical scheme using the exponential map of the manifold. I will also present an energy dissipation property and convergence result.

2019年12月16日（月）立命館大学幾何学セミナー

2019.12.10 Tue up

<<立命館大学幾何学セミナー>>

日時：2019年12月16日（月） 16:30～18:00

タイトル：Semitoric systems in geometry and dynamics

講演者：Sonja Hohloch （University of Antwerp）

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

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.

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).

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