## 過去の記録

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 122号室

Approximations of singular stochastic PDEs and their global well-posedness (特異な確率偏微分方程式の近似とその時間大域的適切性） (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

Analysis for Viscosity Solutions with Special Emphasis on Anomalous Effects (不規則効果を強調した粘性解析） (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

Analysis of the minimal travelling wave speed via the methods of Young measures （進行波の最小速度のYoung 測度による解析） (JAPANESE)

#### 博士論文発表会

9:15-10:30   数理科学研究科棟(駒場) 126号室

Twist maps on quantized coordinate algebras (量子座標環における捻り写像） (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
Gantsooj Batzaya 氏 (東京大学大学院数理科学研究科)
On simultaneous approximation to a pair of powers of a real number by rational numbers (実数の冪の対の有理数による同時近似について）

#### 博士論文発表会

12:45-14:00   数理科学研究科棟(駒場) 126号室

Fukaya categories, surface Lefschetz fibrations, and Koszul duality theory (Fukaya 圏、曲面Lefschetz 束、Koszul 双対について） (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

Partially ordered sets, order complexes and CAT(0) properties (半順序集合，順序複体，及びCAT(0) 性）
(JAPANESE)

### 2017年01月30日(月)

#### 東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

フラクタル格子上の長距離浸透モデルとランダムウォーク

### 2017年01月27日(金)

#### 代数幾何学セミナー

14:00-17:30   数理科学研究科棟(駒場) 122号室

Luca Tasin 氏 (Roma Tre University) 14:00-15:30
On the number and boundedness of minimal models of general type (English)
[ 講演概要 ]
In this talk I will explain that the number of minimal models yields a constructible function on the base of any family of varieties of general type. From this it follows that the number of minimal models of a variety of general type can be bounded in terms of its volume. I will also show that in any dimension minimal models of general type and bounded volume form a bounded family. This is based on a joint work with D. Martinelli and S. Schreieder.
Roberto Svaldi 氏 (University of Cambridge/SISSA) 16:00-17:30
[ 講演概要 ]
The classification of foliated surfaces by Brunella, McQuillan and Mendes carries many similarities with Enriques-Kodaira classification of surfaces but also many important differences. I will discuss an alternative classification scheme where the role of differential forms along the leaves is replaced by differential forms along the leaves with values in fractional powers of the conormal bundle of the foliation. In this alternative setup one obtains a classification of foliated surfaces closer to the usual Enriques-Kodaira classification. If time permits, I will show how to apply this alternative classification to describe the Zariski closure of the set foliations which admit rational first integral of bounded genus in families of foliated surfaces. Joint work with Jorge Vitorio Pereira.
[ 講演参考URL ]
https://www.dpmms.cam.ac.uk/~rs872/

### 2017年01月26日(木)

#### 統計数学セミナー

13:00-16:00   数理科学研究科棟(駒場) 052号室
Ioane Muni Toke 氏 (Centrale Supelec Paris)
High-frequency financial data : trades and quotes databases, order flows and time resolution I, II, III

[ 講演概要 ]
I present some of the challenges associated with preparing high-frequency trades and quotes databases for statistics purposes. In a first part, I investigate TRTH tick-by-tick data on three exchanges (Paris, London and Frankfurt) and on a five-year span. I analyse the performances of a procedure of reconstruction of orders flows. This turns out to be a　forensic tool assessing the quality of the database: significant technical changes affecting the exchanges are　tracked through the data. Moreover, the choices made when reconstructing order flows may have consequences on the quantitative models that are calibrated afterwards on such data. I also provide a refined look at the Lee–Ready procedure and its optimal lags. Findings are in line with both financial reasoning and the analysis of an illustrative Poisson model. In a second part, I investigate Nikkei-packaged Tokyo-traded ETF data. The application the order flow reconstruction procedure underlines the differences between the TRTH and Nikkei data. In a brief last part, we will discuss the time resolution of these databases and the potential problems arising when modelling a limit order book with simple point processes.

### 2017年01月24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

[ 講演概要 ]
We show that the presence of a non-contractible Hamiltonian one-periodic trajectory in a closed symplectic manifold yields the existence of infinitely many non-contractible periodic trajectories, provided that the symplectic form is aspherical and the fundamental group is virtually abelian. Moreover, we also show that a similar statement holds for closed monotone or negative monotone symplectic manifolds having virtually abelian fundamental groups. These results are certain generalizations of works by Ginzburg and Gurel who proved a similar statement holds for atoroidal or toroidally monotone closed symplectic manifolds. The proof is based on the machinery of filtered Floer--Novikov homology for non-contractible periodic trajectories.

#### トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室

Quantitative shadowing property, shadowable points, and local properties of topological dynamical systems (JAPANESE)
[ 講演概要 ]
Shadowing property has been one of the key notions in topological hyperbolic dynamics, which is also common since C^0-generic homeomorphisms on a smooth closed manifold satisfy the property for instance. In this talk, the shadowing property in relation to other chaotic or non-chaotic properties of dynamical systems (entropy, sensitivity, equicontinuity, etc.) is discussed. Also, we introduce an idea of localizing and quantifying the shadowing property following the recent work of Morales, and present some of its consequences. The idea is shown to be effective for the description of local properties of dynamical systems.

### 2017年01月23日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

A unified proof of Cousin I, II and d-bar equation on domains of holomorphy (JAPANESE)
[ 講演概要 ]
Oka's J\^oku-Ik\^o says that holomorphic functions on a complex submanifold of a polydisk extend holomorphically to the whole polydisk. By making use of Oka's J\^oku-Ik\^o we give a titled proof with introducing an argument that represents one of the three cases.
The proof is a modification of the cube dimension induction, used in the proof of Oka's Syzygy for coherent sheaves.

### 2017年01月19日(木)

#### 統計数学セミナー

13:00-15:30   数理科学研究科棟(駒場) 052号室
Feng Chen 氏 (University of New South Wales)
Talk 1:Likelihood inference for a continuous time GARCH model
Talk 2:Nonparametric Estimation for Self-Exciting Point Processes: A Parsimonious Approach
[ 講演概要 ]
Talk 1:The continuous time GARCH (COGARCH) model of Kluppelberg, Lindner and Maller (2004) is a natural extension of the discrete time GARCH(1,1) model which preserves important features of the GARCH model in the discrete-time setting. For example, the COGARCH model is driven by a single source of noise as in the discrete time GARCH model, which is a Levy process in the COGARCH case, and both models can produced heavy tailed marginal returns even when the driving noise is light-tailed. However, calibrating the COGARCH model to data is a challenge, especially when observations of the COGARCH process are obtained at irregularly spaced time points. The method of moments has had some success in the case with regularly spaced data, yet it is not clear how to make it work in the more interesting case with irregularly spaced data. As a well-known method of estimation, the maximum likelihood method has not been developed for the COGARCH model, even in the quite simple case with the driving Levy process being compound Poisson, though a quasi-maximum likelihood (QML)method has been proposed. The challenge with the maximum likelihood method in this context is mainly due to the lack of a tractable form for the likelihood. In this talk, we propose a Monte Carlo method to approximate the likelihood of the compound Poisson driven COGARCH model. We evaluate the performance of the resulting maximum likelihood (ML) estimator using simulated data, and illustrate its application with high frequency exchange rate data. (Joint work with Damien Wee and William Dunsmuir).

Talk 2:There is ample evidence that in applications of self-exciting point process (SEPP) models, the intensity of background events is often far from constant. If a constant background is imposed, that assumption can reduce significantly the quality of statistical analysis, in problems as diverse as modelling the after-shocks of earthquakes and the study of ultra-high frequency financial data. Parametric models can be
used to alleviate this problem, but they run the risk of distorting inference by misspecifying the nature of the background intensity function. On the other hand, a purely nonparametric approach to analysis
leads to problems of identifiability; when a nonparametric approach is taken, not every aspect of the model can be identified from data recorded along a single observed sample path. In this paper we suggest overcoming this difficulty by using an approach based on the principle of parsimony, or Occam's razor. In particular, we suggest taking the point-process intensity to be either a constant or to have maximum differential entropy. Although seldom used for nonparametric function estimation in other settings, this approach is appropriate in the context of SEPP models. (Joint work with the late Peter Hall.)

### 2017年01月17日(火)

#### トポロジー火曜セミナー

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

On an application of the Fukaya categories to the Koszul duality (JAPANESE)
[ 講演概要 ]
In this talk, we compute an A-Koszul dual of path algebras with relations over the directed An-type quivers via the Fukaya categories of exact Riemann surfaces.

The Koszul duality is originally a duality between certain quadratic algebras called Koszul algebras. In this talk, we are interested in the case when A is not a quadratic algebra, i.e. the case when A is defined as a quotient algebra of tensor algebra devided by higher degree relations.

The definition of Koszul duals for such algebras, A-Koszul duals, are given by some people, for example, D. M. Lu, J. H. Palmieri, Q. S. Wu, J. J. Zhang. However, the computation for a concrete examples is hard. In this talk, we use the Fukaya categories of exact Riemann surfaces to compute A-Koszul duals. Then, we understand the Koszul duality as a duality between higher products and relations.

### 2017年01月16日(月)

#### 統計数学セミナー

16:50-18:00   数理科学研究科棟(駒場) 052号室

Profile likelihood approach to a large sample distribution of estimators in joint mixture model of survival and longitudinal ordered data
[ 講演概要 ]
We consider a semiparametric joint model that consists of item response and survival components, where these two components are linked through latent variables. We estimate the model parameters through a profile likelihood and the EM algorithm. We propose a method to derive an asymptotic variance of the estimators in this model.

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Dinh Tuan Huynh 氏 (大阪大学)
A geometric second main theorem (ENGLISH)
[ 講演概要 ]
Using Ahlfors’ theory of covering surfaces, we establish a Cartan’s type Second Main Theorem in the complex projective plane with 1–truncated counting functions for entire holomorphic curves which cluster on an algebraic curve.

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 117号室

[ 講演概要 ]
Scaleとはボイラなどの内側にできる湯あかのことをいう。その成分は主としてカルシウムおよびマグネシウムの硫酸塩、炭酸塩、ケイ酸塩である。ボイラ内の対流の障害になるほか、熱伝導率が小さいので伝熱量が減るばかりでなく、伝熱面の過熱破損の原因となる。古くからそれらの弊害を除去すべく種々の装置が開発されてきた。しかし、現在に至ってもそれらの決定版と言われるのは見い出し難い状況にある。

しかしながら、上記装置がscale形成抑止に何故有効であるか、そのメカニズムは未だ解明されていない。我々はこの現象に対して基本的仮説を提示して、その原理の解明を試みる。そのカギとなるのは炭酸カルシウム結晶の表面自由エネルギーの制御にある。この仕組みの展開には数理モデルの構築とその数値解析が重要な役割を担っている。

#### 東京確率論セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室

Monotonicity and rigidity of the W-entropy on RCD (0,N) spaces (日本語)

### 2017年01月12日(木)

#### 統計数学セミナー

13:00-15:00   数理科学研究科棟(駒場) 052号室
Emanuele Guidotti 氏 (Milan University)
yuimaGUI: a Graphical User Interface for the yuima Package
[ 講演概要 ]
The yuimaGUI package provides a user-friendly interface for yuima. It greatly simplifies tasks such as estimation and simulation of stochastic processes and it also includes additional tools. Some of them:
data retrieval: stock prices and economic indicators
time series clustering
change point analysis
After a general overview of the whole interface, the yuimaGUI will be shown in real-time. All the settings and the inner workings will be discussed in detail. During this second part, you are kindly invited to ask questions whenever you feel that some problem may arise.

### 2017年01月11日(水)

#### 代数学コロキウム

18:00-19:00   数理科学研究科棟(駒場) 056号室
Lei Fu 氏 (Tsinghua University)
Deformation and rigidity of $\ell$-adic sheaves (English)
[ 講演概要 ]
Let $X$ be a smooth connected algebraic curve over an algebraically closed field, let $S$ be a finite closed subset in $X$, and let $F_0$ be a lisse $\ell$-torsion sheaf on $X-S$. We study the deformation of $F_0$. The universal deformation space is a formal scheme. Its generic fiber has a rigid analytic space structure. By studying this rigid analytic space, we prove a conjecture of Katz which says that if a lisse $\overline{Q}_\ell$-sheaf $F$ is irreducible and physically rigid, then it is cohomologically rigid in the sense that $\chi(X,j_*End(F))=2$, where $j:X-S\to X$ is the open immersion.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理，Morningside Center of MathematicsとIHESの双方向同時中継で行います.)

### 2017年01月10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

Stability of anti-canonically balanced metrics (JAPANESE)
[ 講演概要 ]
Donaldson introduced "anti-canonically balanced metrics" on Fano manifolds, which is a finite dimensional analogue of Kähler-Einstein metrics. It is proved that anti-canonically balanced metrics are critical points of the quantized Ding functional.

We first study the slope at infinity of the quantized Ding functional along Bergman geodesic rays. Then, we introduce a new algebro-geometric stability of Fano manifolds based on the slope formula, and show that the existence of anti-canonically balanced metrics implies our stability. The relationship between the stability and others is also discussed.

This talk is based on a joint work with R. Takahashi (Tohoku Univ).

#### トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室

Topological Invariants and Corner States for Hamiltonians on a Three Dimensional Lattice (JAPANESE)
[ 講演概要 ]
In condensed matter physics, a correspondence between two topological invariants defined for a gapped Hamiltonian is well-known. One is defined for such a Hamiltonian on a lattice (bulk invariant), and the other is defined for its restriction onto a subsemigroup (edge invariant). The edge invariant is related to the wave functions localized near the edge. This correspondence is known as the bulk-edge correspondence. In this talk, we consider a variant of this correspondence. We consider a periodic Hamiltonian on a three dimensional lattice (bulk) and its restrictions onto two subsemigroups (edges) and their intersection (corner). We will show that, if our Hamiltonian is "gapped" in some sense, we can define a topological invariant for the bulk and edges. We will also define another topological invariant related to the wave functions localized near the corner. We will explain that there is a correspondence between these two topological invariants by using the six-term exact sequence associated to the quarter-plane Toeplitz extension obtained by E. Park.

### 2016年12月22日(木)

#### 東京無限可積分系セミナー

14:00-17:30   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

その後 Baker によりそのようなレンズ空間が完全に決定された．

て得られた結果を紹介する．

たす．

Schur分割定理の一般化について (JAPANESE)
[ 講演概要 ]
Rogers-Ramanujan（第1）恒等式は「隣接するパートの差が 2

ような n の分割は、各パートが mod 5で± 1であるようなnの分割と同数存在す
る」
という分割定理と同値であるが、Schurは1926年に後者の mod 6 版を発見した。

いて、
この定理を一般の奇数p¥geq 3に拡張したので報告する。p=3 の場合が Schur 分

p=5 の場合は、Andrews によって1970年代にRogers-Ramanujan 分割定理の
3パラメータ拡張に関連して予想され、1994年に Andrews-Bessenrodt-Olsson に
よって計算機を援用して証明された分割定理に対応する。

### 2016年12月20日(火)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Nader Masmoudi 氏 (Courant Institute, NYU)
On the stability of the 3D Couette Flow (English)
[ 講演概要 ]
We will discuss the dynamics of small perturbations of the plane, periodic Couette flow in the 3D incompressible Navier-Stokes system at high Reynolds number. For sufficiently regular initial data, we determine the stability threshold for small perturbations and characterize the long time dynamics of solutions near this threshold. For rougher data, we obtain an estimate of the stability threshold which agrees closely with numerical experiments. The primary linear stability mechanism is an anisotropic enhanced dissipation resulting from the mixing caused by the large mean shear. There is also a linear inviscid damping similar to the one observed in 2D. The main linear instability is a non-normal instability known as the lift-up effect. There is clearly a competition between these linear effects. Understanding the variety of nonlinear resonances and devising the correct norms to estimate them form the core of the analysis we undertake. This is based on joint works with Jacob Bedrossian and Pierre Germain.