## 過去の記録

### 2018年02月04日(日)

#### 統計数学セミナー

12:00-18:00   数理科学研究科棟(駒場) 118号室
Yukai Yang 氏 (Uppsala University) 12:30-15:00
Nonlinear Economic Time Series Models

[ 講演概要 ]
The lecture goes through several chapters in the book “Modelling Nonlinear Economic Time Series” by Teräsvirta, Tjøstheim and Granger in 2010. The lecture serves as an introduction for the students and researchers who are interested in this area. It introduces a number of examples of families of nonlinear time series parametric models in economic theory. It also talks about testing linearity against parametric alternatives with the presence of a characterization of the identification problem in many situations. Different ways of solving the identification problem are presented and their merits and disadvantages are discussed.
Yuliia Mishura 氏 (The Taras Shevchenko National University of Kiev ) 15:30-18:00
Analytic, representation and statistical aspects related to fractional Gaussian processes.

[ 講演概要 ]
We consider the properties of fractional Gaussian processes whose covariance function is situated between two self-similarities, or, in other words, these processes belong to the generalized quasi-helix, according to geometric terminology of Kahane. For such processes we consider the two-sided bounds for maximal functionals and the representation results. We consider stochastic differential equations involving fractional Brownian motion and present also several results on statistical estimations for them.

### 2018年02月02日(金)

#### 統計数学セミナー

13:30-14:40   数理科学研究科棟(駒場) 052号室
Ioane Muni Toke 氏 (Centrale Supelec Paris)
Estimation of ratios of intensities in a Cox-type model of limit order books
[ 講演概要 ]
We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The Cox-like intensities of the counting processes of events are assumed to share an unobserved and unspecified baseline intensity, which in finance can be identified to a global market activity affecting all events. The model is formulated in terms of relative responses of the intensities to covariates, and relative parameters can be estimated by quasi likelihood maximization. Consistency and asymptotic normality of the estimators are proven. Computationally intensive inferences are run on large samples of tick-by-tick data (35+ stocks and 220+ trading days, adding to more than one billion events). Penalization methods are also investigated. Results of the model are interpreted in terms of probability of occurrence of events. Excellent agreement with empirical data is found. Estimated model reproduces known empirical facts on imbalance, spread and queue sizes, and helps identifying trading signals of interests on a given stock.

Joint work with N.Yoshida.

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 118号室

A study on (g,K)- modules over commutative rings
(可換環上の(g,K)加群の研究)
(JAPANESE)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 122号室

An invariant of 3-manifolds via homology cobordisms and knots in lens spaces
(ホモロジーコボルディズムを用いた3次元多様体の不変量とレンズ空間内の結び目)
(JAPANESE)

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 122号室

An Application of the F-method to Duflo-Corwin-Greenleaf's Polynomial Conjecture
(Duflo-Corwin-Greenleafの多項式予想に対するF-methodの適用)
(JAPANESE)

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 118号室

Numerical analysis for evolution equations
(発展方程式に対する数値解析)
(JAPANESE)

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 122号室

Continuous Analogue of the Existence Problem of Compact Clifford-Klein Forms
(コンパクトClifford-Klein形の存在問題の連続類似)
(JAPANESE)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 122号室

Actions on noncommutative tori and classification of the crossed products
(非可換トーラス上の作用と接合積の分類)
(JAPANESE)

### 2018年02月01日(木)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 122号室

A new relationship between the dilatation of pseudo-Anosov braids and fixed point theory
(擬アノソフ組みひもの拡張率と固定点理論との新たな関係)
(JAPANESE)

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 122号室
Jimenez Pascual, Adrian 氏 (東京大学大学院数理科学研究科)
On wrapping number, adequacy and the crossing number of satellite knots
(ラッピング数、充足性とサテライト結び目の最小交点数について)
(JAPANESE)

#### 博士論文発表会

10:45-12:00   数理科学研究科棟(駒場) 126号室

On L2-extension theorems and singularities of plurisubharmonic functions in complex analysis and geometry
(複素解析・複素幾何におけるL2拡張定理と多重劣調和関数の特異性について)
(JAPANESE)

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 118号室

Criteria for good reduction of hyperbolic polycurves
(多重双曲的曲線の良還元判定条件)
(JAPANESE)

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 122号室

Creation of mathematical methods for the social cooperation:
solutions of problems in the steel industry, environments and the traffic flow
(社会連携における数学的手法の創造：製鉄業、環境ならびに交通流についての課題の解決)
(JAPANESE)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 118号室

Studies on integral representations of GKZ hypergeometric functions
(GKZ超幾何函数の積分表示に関する研究)
(JAPANESE)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 122号室

Wrapping projections and decompositions of Kleinian groups
(Wrapping射影とクライン群の分解について)
(JAPANESE)

#### 博士論文発表会

14:15-15:30   数理科学研究科棟(駒場) 126号室

Estimation and statistical testing of the correlation between latent processes
(潜在確率過程間の相関の推定及び統計的検定)
(JAPANESE)

#### 博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 118号室

Validity of formal expansions for singularly perturbed competition-diffusion systems
(競争拡散系の特異摂動に対する形式的漸近展開の正当性)
(JAPANESE)

#### 博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 122号室

Applications of Microlocal Sheaf Theory to Symplectic Geometry in Cotangent Bundles
(余接束のシンプレクティック幾何への超局所層理論の応用)
(JAPANESE)

#### 博士論文発表会

15:45-17:00   数理科学研究科棟(駒場) 126号室

Homology pro stability for Tor-unital pro rings
（捻単位的副環のホモロジー副安定性）
(JAPANESE)

#### 博士論文発表会

17:15-18:30   数理科学研究科棟(駒場) 118号室

Mathematical foundation of Isogeometric Analysis for evolution problems
(発展問題に対するIsogeometric Analysisの数学的基礎)
(JAPANESE)

#### 博士論文発表会

17:15-18:30   数理科学研究科棟(駒場) 122号室

A formula for the action of Dehn twists on HOMFLY-PT skein modules and its applications
(HOMFLY-PT スケイン加群への Dehn ツィストの作用の公式とその応用)
(JAPANESE)

#### 博士論文発表会

17:15-18:30   数理科学研究科棟(駒場) 126号室

Quasi-integrable extensions of the discrete Toda lattice equation
(離散戸田格子方程式の準可積分拡張)
(JAPANESE)

### 2018年01月30日(火)

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

Persistence-like distance on Tamarkin's category and symplectic displacement energy (JAPANESE)
[ 講演概要 ]
The microlocal sheaf theory due to Kashiwara and Schapira can be regarded as Morse theory with sheaf coefficients. Recently it has been applied to symplectic geometry, after the pioneering work of Tamarkin. In this talk, I will propose a new sheaf-theoretic method to estimate the displacement energy of compact subsets in cotangent bundles. In the course of the proof, we introduce a persistence-like pseudo-distance on Tamarkin's sheaf category. This is a joint work with Tomohiro Asano.

### 2018年01月29日(月)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 126号室

Tingley's problem for operator algebras

#### 東京確率論セミナー

16:00-17:30   数理科学研究科棟(駒場) 128号室

Radial processes on RCD${}^*(K,N)$-spaces (JAPANESE)
[ 講演概要 ]

この講演は東北大学の桑田和正氏との共同研究に基づく。