## 過去の記録

### 2018年03月26日(月)

#### FMSPレクチャーズ

10:00-12:00   数理科学研究科棟(駒場) 002号室

Jørgen Ellegaard Andersen 氏 (Aarhus University)
Geometric Recursion (ENGLISH)
[ 講演概要 ]
Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form on moduli spaces of flat connections for general compact simple Lie groups. We shall also discuss the process which establishes that any application of Topological Recursion can be lifted to a Geometric Recursion setting involving continuous functions on Teichmüller space, where the connection back to Topological Recursion is obtained by integration over the moduli space of curve. The work
presented is joint with G. Borot and N. Orantin.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Andersen.pdf

### 2018年03月23日(金)

#### FMSPレクチャーズ

10:00-12:00   数理科学研究科棟(駒場) 002号室

Jørgen Ellegaard Andersen 氏 (Aarhus University)
Geometric Recursion (ENGLISH)
[ 講演概要 ]
Geometric Recursion is a very general machinery for constructing mapping class group invariants objects associated to two dimensional surfaces. After presenting the general abstract definition we shall see how a number of constructions in low dimensional geometry and topology fits into this setting. These will include the
Mirzakhani-McShane identies, mapping class group invariant closed forms on Teichmüller space (including the Weil-Petterson symplectic form) and the Goldman symplectic form on moduli spaces of flat connections for general compact simple Lie groups. We shall also discuss the process which establishes that any application of Topological Recursion can be lifted to a Geometric Recursion setting involving continuous functions on Teichmüller space, where the connection back to Topological Recursion is obtained by integration over the moduli space of curve. The work presented is joint with G. Borot and N. Orantin.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Andersen.pdf

### 2018年03月19日(月)

#### 数理人口学・数理生物学セミナー

17:00-18:00   数理科学研究科棟(駒場) 509号室

Age構造付き増殖過程の大偏差原理を用いた解析
[ 講演概要 ]

### 2018年03月15日(木)

#### 統計数学セミナー

16:00-17:10   数理科学研究科棟(駒場) 052号室
Stefano Iacus 氏 (University of Milan)
On Hypotheses testing for discretely observed SDE (Joint work with Alessandro De Gregorio, University of Rome)
[ 講演概要 ]
In this talk we consider parametric hypotheses testing for discretely observed ergodic diffusion processes. We present the different test statistics proposed in literature and recall their asymptotic properties. We also compare the empirical performance of different tests in the case of small sample sizes.

### 2018年03月13日(火)

#### 講演会

10:00-11:00   数理科学研究科棟(駒場) 126号室

GSpにおけるDeligne-Lusztig多様体とaffine Deligne-Lusztig多様体との比較

[ 講演概要 ]
Deligne-Lusztig理論とは、有限体上の簡約代数群の有理点の表現を、Deligne-Lusztig多様体と呼ばれる代数多様体のエタールコホモロジーに実現する理論であった。Lusztigは、この理論の非Archimedes的局所体K上での類似の存在を予想した。しかし、Deligne-Lusztig多様体の局所体上の直接の類似物は、アプリオリにはscheme構造を持たないという問題がある。

### 2018年03月12日(月)

#### Lie群論・表現論セミナー

15:00-16:30   数理科学研究科棟(駒場) 126号室
Christian Ikenmeyer 氏 (Max-Planck-Institut fur Informatik)
Plethysms and Kronecker coefficients in geometric complexity theory
[ 講演概要 ]
Research on Kronecker coefficients and plethysms gained significant momentum when the topics were connected with geometric complexity theory, an approach towards computational complexity lower bounds via algebraic geometry and representation theory. This talk is about several recent results that were obtained with geometric complexity theory as motivation, namely the NP-hardness of deciding the positivity of Kronecker coefficients and an inequality between rectangular Kronecker coefficients and plethysm coefficients. While the proof of the former statement is mainly combinatorial, the proof of the latter statement interestingly uses insights from algebraic complexity theory. As far as we know algebraic complexity theory has never been used before to prove an inequality between representation theoretic multiplicities.

### 2018年03月10日(土)

#### 談話会・数理科学講演会

11:00-12:00   数理科学研究科棟(駒場) 大講義室号室

[ 講演概要 ]

#### 談話会・数理科学講演会

13:00-14:00   数理科学研究科棟(駒場) 大講義室号室

K安定性と幾何学的非線形問題 (JAPANESE)
[ 講演概要 ]
K安定性は代数幾何における幾何学的不変式論（GIT）の安定性として定式化されたものであるが，アイデアの端緒は Kazdan-Warner が見出したある非線形偏微分方程式の可解性の障害にある．この非線形問題は微分幾何学的に表現すると，2次元単位球面に滑らかな関数 k を任意に与えたとき，計量 g に適当な正の関数 f をかけて得られる計量 fg が k をガウス曲率になるように，f を決めることができるか，という問題である．これは Nirenberg の問題と呼ばれ，現時点でも完全な答えは得られていない．2次元球面を１次元複素射影空間とみなし，更に Fano 多様体の特別な場合とみなして，Fano 多様体の GIT 安定性として定式化したのは Gang Tian であり（1997），さらに一般の偏極多様体に一般化したのは Simon K. Donaldson である（2002）．GIT 安定性はモーメント写像を用いた描像があり，有限次元シンプレクティック幾何の形式的議論が，非線形偏微分方程式を解くにあたっての関数空間における無限次元シンプレクティック幾何的な議論の適切な方向を探る指針を与える．Fano 多様体においては，K安定性がモンジュ・アンペール方程式の可解性と同値であり，従ってケーラー・アインシュタイン計量の存在と同値であることが2012年頃，Chen-Donaldson-Sun と Tian によって証明された．モーメント写像を用いた描像を用いると，他の色々な非線形問題においても同じパターンで，K安定性と可解性の同値性を証明する問題として定式化される．

#### 談話会・数理科学講演会

14:30-15:30   数理科学研究科棟(駒場) 大講義室号室

[ 講演概要 ]

#### 談話会・数理科学講演会

16:00-17:00   数理科学研究科棟(駒場) 大講義室号室

(JAPANESE)
[ 講演概要 ]

### 2018年03月09日(金)

#### 講演会

13:30-14:30   数理科学研究科棟(駒場) 056号室
Luc Illusie 氏 (パリ南大学名誉教授)
Sliced nearby cycles and duality, after W. Zheng (ENGLISH)
[ 講演概要 ]
In the early 1980's Gabber proved duality for nearby cycles and, by a different method, Beilinson proved duality for vanishing cycles in the strictly local case (up to a twist of the inertia action on the tame part). Recently W. Zheng found a simple proof of a result, conjectured by Deligne, which implies them both, and extended it over finite dimensional excellent bases. I will explain the main ideas of his work, which relies on new developments, due to him, of Deligne's theory of fibered and oriented products.

### 2018年03月02日(金)

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 270号室
Arnaud Gloter 氏 (Université d'Evry Val d'Essonne)
"Estimating functions for SDE driven by stable Lévy processes"
Joint work with Emmanuelle Clément (Ecole Centrale)
[ 講演概要 ]
In this talk we will discuss about parametric inference for a stochastic differential equation driven by a pure-jump Lévy process, based on high frequency observations on a fixed time period. Assuming that the Lévy measure of the driving process behaves like that of an α-stable process around zero, we propose an estimating functions based method which leads to asymptotically efficient estimators for any value of α ∈ (0, 2).

### 2018年02月23日(金)

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

ても大きく進展している。本講演では、極小モデル理論について概説した後、時

#### FMSPレクチャーズ

13:30-15:00   数理科学研究科棟(駒場) 002号室

Etienne Ghys 氏 (ENS de Lyon)
The topology of singular points of real analytic curves (ENGLISH)
[ 講演概要 ]
In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

### 2018年02月22日(木)

#### FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 117号室

Etienne Ghys 氏 (ENS de Lyon)
The topology of singular points of real analytic curves (ENGLISH)
[ 講演概要 ]
In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

### 2018年02月21日(水)

#### FMSPレクチャーズ

15:00-16:30   数理科学研究科棟(駒場) 117号室

Etienne Ghys 氏 (ENS de Lyon)
The topology of singular points of real analytic curves (ENGLISH)
[ 講演概要 ]
In the neighborhood of a singular point, a germ of real analytic curve in the plane consists of a finite number of branches. Each of these branches intersects a small circle around the singular point in two points. Therefore, the local topology is described by a chord diagram : an even number of points on a circle paired two by two. Not all chord diagrams come from a singular point. The main purpose of this mini course is to give an complete description of those ‘’analytic ? chord diagrams. On our way, we shall meet some interesting concepts from computer science, graph theory and operads.
[ 参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Ghys.pdf

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 122号室
Tea: Common Room 16:30-17:00
Gwénaël Massuyeau 氏 (Université de Bourgogne)
The category of bottom tangles in handlebodies, and the Kontsevich integral (ENGLISH)
[ 講演概要 ]
Habiro introduced the category B of « bottom tangles in handlebodies », which encapsulates the set of knots in the 3-sphere as well as the mapping class groups of 3-dimensional handlebodies. There is a natural filtration on the category B defined using an appropriate generalization of Vassiliev invariants. In this talk, we will show that the completion of B with respect to the Vassiliev filtration is isomorphic to a certain category A which can be defined either in a combinatorial way using « Jacobi diagrams », or by a universal property via the notion of « Casimir Hopf algebra ». Such an isomorphism will be obtained by extending the Kontsevich integral (originally defined as a knot invariant) to a functor Z from B to A. This functor Z can be regarded as a refinement of the TQFT-like functor derived from the LMO invariant and, if time allows, we will evoke the topological interpretation of the « tree-level » of Z. (This is based on joint works with Kazuo Habiro.)

### 2018年02月19日(月)

#### 数値解析セミナー

15:00-16:00   数理科学研究科棟(駒場) 056号室
Michael Plum 氏 (Karlsruhe Insitute of Technology)
Existence, multiplicity, and orbital stability for travelling waves in a nonlinearly supported beam (English)
[ 講演概要 ]
For a nonlinear beam equation with exponential nonlinearity, we prove existence of at least 36 travelling wave solutions for the specific wave speed c=1.3. Our proof makes heavy use of computer assistance: starting from numerical approximations, we use a fixed point argument to prove existence of solutions "close to" the approximate ones. Furthermore we investigate the orbital stability of these solutions by making use of both analytical and computer-assisted techniques.

#### 数値解析セミナー

16:15-17:15   数理科学研究科棟(駒場) 056号室

An approach to computer-assisted existence proofs for nonlinear space-time fractional parabolic problems (English)
[ 講演概要 ]
We consider an initial boundary value problem for a space-time fractional parabolic equation, which includes the fractional Laplacian, i.e. a nonlocal operator. We treat a corresponding local problem which is obtained by the Caffarelli-Silvestre extension technique, and show how to enclose a solution of the extended problem by computer-assisted means.

### 2018年02月14日(水)

#### 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
Valerio Proietti 氏 (Copenhagen Univ.)
Index theory on the Mishchenko bundle (English)

### 2018年02月06日(火)

#### 東京無限可積分系セミナー

15:00-17:30   数理科学研究科棟(駒場) 002号室

１次元量子臨界系のサイン二乗変形 (ENGLISH)
[ 講演概要 ]
サイン二乗変形(SSD)とは、量子系のハミルトニアンの局所的エネルギースケールを、サイン二乗関数にしたがって空間的方向に変調させる変形操作である。SSDにより、一様周期境界条件を課した系のハミルトニアンは、開放境界条件を課した空間的に非一様なハミルトニアンへと変形される。しかしながら、空間次元１次元で系が臨界的な場合には、この変形後のハミルトニアンの基底状態は、変形前の一様周期的な基底状態からほとんど変化しないということが、現在までに明らかにされている。特に講演者は、臨界的なXYスピン鎖や横磁場Ising模型においては、両者の基底状態が厳密に一致することを示している
[1,2,3]。また、ディラック・フェルミオン系や一般の(1+1)次元の共形場理論についても、適切にSSDを定義すれば、やはり一様周期系とSSD系の基底状態が一致するという結果を紹介する。時間が許せば、その他の最近の結果
[4,5] や、SSD系の励起状態についての結果についても紹介する。

[1] H. Katsura, J. Phys. A: Math. Theor. 44, 252001 (2011).
[2] H. Katsura, J. Phys. A: Math. Theor. 45, 115003 (2012).
[3] I. Maruyama, H. Katsura, T. Hikihara, Phys. Rev. B 84, 165132 (2011).
[4] K. Okunishi and H. Katsura, J. Phys. A: Math. Theor. 48, 445208 (2015).
[5] S. Tamura and H. Katsura, Prog. Theor. Exp. Phys 2017, 113A01 (2017).

モジュラー不変性をもつ $N=2$ 頂点作用素超代数の表現に
ついて (ENGLISH)
[ 講演概要 ]
よいクラスの頂点作用素超代数の表現の指標はモジュラー不変性という顕著な性質を示す．この性質の応用として，中心電荷が$c_{p,1}=3(1-2/p)$である$N=2$頂点作用素超代数のフュージョン則は，モジュラー$S$行列から Verlinde公式によって計算されることが知られている（脇本実氏とD. Adamovic氏の結果による）．本セミナーでは，互いに素な$2$以上の整数組$(p,p')$を用いて中心電荷が$c_{p,p'}:=3(1-2p'/p)$と表わされる場合に，然るべき意味でモジュラー不変性を示す新たな$N=2$頂点作用素超代数の表現族を紹介する．また，Creutzig--Ridoutによって提案されたVerlinde公式の一般化を踏まえて，フュージョン則の計算への応用を議論する．

### 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)