## 過去の記録

#### FMSPレクチャーズ

17:00-18:00   数理科学研究科棟(駒場) 118号室
Oleg Emanouilov 氏 (Colorado State University)
Conditional stability in Gelfand-Levitan problem (ENGLISH)
[ 講演概要 ]
We consider the Laplace-Beltrami operator in the bounded domain on the plane.
The eigenvalues and the traces of the eigenfunctions on part of the boundary are given.
We obtain the double logarithmic stability for the determination of metric up to the gauge equivalence.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov161109.pdf

### 2016年11月08日(火)

#### 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) 056号室
Tea: Common Room 16:30-17:00

Second mod 2 homology of Artin groups (JAPANESE)
[ 講演概要 ]
After a brief survey on the K($\pi$,1) conjecture and homology of Artin groups,I will introduce our recent result: we determined second mod 2 homology of arbitrary Artin groups without assuming the K($\pi$,1)-conjecture. The key ingredients are Hopf's formula and a result of Howlett on Schur multipliers of Coxeter groups. This is a joint work with Ye Liu.

#### FMSPレクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (5) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### FMSPレクチャーズ

13:15-14:15   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (6) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### 代数幾何学セミナー

15:30-17:00   数理科学研究科棟(駒場) 118号室
いつもと部屋が異なります。

Minimal model theory for relatively trivial log canonical pairs
[ 講演概要 ]
The good minimal model conjecture is an important open problem in the birational geometry, and inductive arguments on the dimension of varieties are useful when we work on this conjecture. In fibration with a log canoinical pair having some good properties, it is expected that the above conjecture for the log canonical pair on total space can be proved by investigating the general fiber and base variety of the fibration. In this talk, I will explain an inductive argument in fibrations with relatively trivial log canonical pairs and introduce some applications of the inductive argument.

### 2016年11月07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

[ 講演概要 ]

### 2016年11月04日(金)

#### FMSPレクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (3) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### FMSPレクチャーズ

13:00-14:00   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (4) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

### 2016年11月02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
Yves André 氏 (CNRS, Institut de Mathématiques de Jussieu)
Direct summand conjecture and perfectoid Abhyankar lemma: an overview (English)
[ 講演概要 ]
According to Hochster's direct summand conjecture (1973), a regular ring R is a direct summand, as an R-module, of every finite extension ring. We shall outline our recent proof which relies on perfectoid techniques. Similar arguments also establish the existence of big Cohen-Macaulay algebras for complete local domains of mixed characteristics.

(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.)

### 2016年11月01日(火)

#### 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) 056号室
Tea: Common Room 16:30-17:00

Higher-dimensional contact manifolds with infinitely many Stein fillings (JAPANESE)
[ 講演概要 ]
A Stein fillings of a given contact manifold is a Stein domain whose boundary is contactomorphic to the given contact manifold.
Open books, Lefschetz fibrations, and mapping class groups of their fibers in particular help us to produce various contact manifolds and their Stein fillings. However, little is known about mapping class groups of higher-dimensional manifolds. This is one of the reasons that it was unknown whether there is a contact manifold of dimension > 3 with infinitely many Stein fillings. In this talk, I will choose a certain symplectic manifold as fibers of open books and Lefschetz fibrations and by using them, construct an infinite family of higher-dimensional contact manifolds with infinitely many Stein fillings.

#### FMSPレクチャーズ

10:30-11:30   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (1) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### FMSPレクチャーズ

13:15-14:15   数理科学研究科棟(駒場) 128号室
Piotr Rybka 氏 (the University of Warsaw)
The BV space in variational and evolution problems (2) (ENGLISH)
[ 講演概要 ]
http://www.ms.u-tokyo.ac.jp/kyoumu/docs/20160907.pdf　を参照
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Rybka.pdf

#### 統計数学セミナー

10:40-11:30   数理科学研究科棟(駒場) 123号室
Yuta Koike 氏 (Tokyo Metropolitan University, JST CREST)
Wavelet-based methods for high-frequency lead-lag analysis
[ 講演概要 ]
We propose a novel framework to investigate the lead-lag effect between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice. This talk is based on a joint work of Prof. Takaki Hayashi (Keio University).

#### 統計数学セミナー

11:30-12:30   数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (University du Luxembourg)
Second order fluctuations for zeros of arithmetic random waves
[ 講演概要 ]
Originally introduced by Rudnick and Wigman (2007), arithmetic random waves are Gaussian Laplace eigenfunctions on the two-dimensional torus. In this talk, I will describe the high-energy behaviour of the so-called « nodal length » (that, is the volume of the zero set) of such random objects, and show that (quite unexpectedly) it is non-central and non-universal. I will also discuss the connected problem of counting the number of intersections points of independent nodal sets (equivalent to « phase singularities » for complex waves) in the high-energy regime. Both issues are tightly connected to the arithmetic study of lattice points on circles. One key concept in our presentation is that of ‘Berry cancellation phenomenon’ (see M.V. Berry, 2002), for which an explanation in terms of chaos expansions and integration by parts (Green formula) will be provided. Based on joint works (GAFA 2016 & Preprint 2016) with D. Marinucci (Rome Tor Vergata), M. Rossi (Luxembourg) and I. Wigman (King’s College, London), and with F. Dalmao (University of Uruguay), I. Nourdin (Luxembourg) and M. Rossi (Luxembourg).

### 2016年10月31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

Henon 写像族のパラメータ空間におけるホースシュー領域について (JAPANESE)
[ 講演概要 ]
パラメータ $(a, b)$ を持つ平面からそれ自身への多項式写像の族 $f_{a, b} : (x, y)\rightarrow (x^2-a-by, x)$ は Henon 写像族と呼ばれ、非線形力学系の最も基本的なクラスとして多くの数学者や物理学者によって研究されてきた。この写像がなす力学系はパラメータ $(a, b)$ の取り方に大きく依存するが、ある部分パラメータ領域から $(a, b)$ を選ぶと、対応する Henon 写像は「ホースシュー」と呼ばれるカオス力学系の典型的なモデルになることが知られている。今からおよそ３５年前に宇敷重広や Christian Mira らは、Henon 写像がホースシューになるようなパラメータ領域の境界がある滑らかな曲線で特徴付けられることを数値的に観察した。今回の講演では、この数値的観察に対する数学的に厳密な証明について説明する。その証明は、Henon 写像の相空間とパラメータ空間を共に複素拡張し、複素力学系や複素幾何のテクニックを精度保証計算と組み合わせることによって得られる。

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 002号室

[ 講演概要 ]

#### 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
Sergey Neshveyev 氏 (Univ. Oslo)
Dual cocycles and equivariant deformation quantization (English)

#### 統計数学セミナー

10:40-11:30   数理科学研究科棟(駒場) 123号室
Nakahiro Yoshida 氏 (University of Tokyo, Institute of Statistical Mathematics, JST CREST)
Martingale expansion revisited
[ 講演概要 ]
The martingale expansion is revisited in this talk. The martingale expansion for a martingale with mixed normal limit evaluates the tangent of the quadratic variation of the martingale and the torsion of an exponential martingale under the measure transform caused by the random limit of the quadratic variation. The martingale expansion has been applied to the realized volatility, quadratic form of an Ito process, p-variation and the QLA estimators of a volatility parametric model. An interpolation in time was used in martingale expansion. We discuss relation between martingale expansion and recently developed asymptotic expansion of Skorohod integrals by interpolation of distributions (a joint work with D. Nualart).

#### 統計数学セミナー

11:30-12:20   数理科学研究科棟(駒場) 123号室
Nobuaki Naganuma 氏 (Osaka University)
Error analysis for approximations to one-dimensional SDEs via perturbation method
[ 講演概要 ]
We consider one-dimensional stochastic differential equations driven by fractional Brownian motions and adopt the Euler scheme, the Milstein type scheme and the Crank-Nicholson scheme to approximate solutions to the equations. We introduce perturbation method in order to analyze errors of the schemes. By using this method, we can express the errors in terms of directional derivatives of the solutions explicitly. We obtain asymptotic error distributions of the three schemes by combining the expression of the errors and the fourth moment theorem. This talk is based on a joint work with Prof. Shigeki Aida (Tohoku University).

#### 統計数学セミナー

13:50-14:40   数理科学研究科棟(駒場) 123号室
Seiichiro Kusuoka 氏 (Okayama University)
Characterization of the convergence in total variation by Stein's method and Malliavin calculus
[ 講演概要 ]
Recently, convergence in distributions and estimates of distances between distributions are studied by means of Stein's equation and Malliavin calculus. However, in known results, the target distributions of the convergence were some specific distributions. In this talk, we extend the target distributions to invariant probability measures of diffusion processes. Precisely speaking, we prepare Stein's equation with respect to invariant measures of diffusion processes and consider the characterization of the convergence to the invariant measure in total variation by applying Malliavin calculus. This is a joint work with Ciprian Tudor.

#### 統計数学セミナー

14:50-15:40   数理科学研究科棟(駒場) 123号室
Teppei Ogihara 氏 (The Institute of Statistical Mathematics, JST PRESTO, JST CREST)
Parameter estimation for diffusion processes with high-frequency observations
[ 講演概要 ]
We study statistical inference for security prices modeled by diffusion processes with high-frequency observations. In particular, we focus on two specific problems on analysis of high-frequency data, that is, nonsynchronous observations and the presence of observation noise called market microstructure noise. We construct a maximum-likelihood-type estimator of parameters, and study their asymptotic mixed normality. We also discuss on asymptotic efficiency of estimators.

#### 統計数学セミナー

15:40-16:30   数理科学研究科棟(駒場) 123号室
Kengo Kamatani 氏 (Osaka University, JST CREST)
Markov chain Monte Carlo for high-dimensional target distribution
[ 講演概要 ]
The Markov chain Monte Carlo (MCMC) algorithms are widely used to evaluate complicated integrals in Bayesian Statistics. Since the method is not free from the curse of dimensionality, it is important to quantify the effect of the dimensionality and establish an optimal MCMC strategy in high-dimension. In this talk, I will review some high-dimensional asymptotics of MCMC initiated by Roberts et. al. 97, and explain some asymptotic properties of the MpCN algorithm. I will also mention some connection to Stein-Malliavin techniques.

#### 統計数学セミナー

16:50-17:40   数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (Universite du Luxembourg)
New Functionals inequalities via Stein's discrepancies
[ 講演概要 ]
I will present a new set of functional inequalities involving the following four parameters associated with a given multidimensional distribution: the relative entropy, the relative Fisher information, the 2-Wasserstein distance, and the Stein discrepancy (which is a natural object arising in the framework of the Malliavin-Stein method on a Gaussian space). Our results improve the classical log-Sobolev inequality, as well Talagrand's transport inequality, and allow one to deduce new quantitative entropic limit theorems on Gaussian spaces. Joint works (JFA 2014 and GAFA 2015) with M. Ledoux (Toulouse), I. Nourdin (Luxembourg) and Y. Swan (Liège).

#### 統計数学セミナー

17:40-18:30   数理科学研究科棟(駒場) 123号室
Giovanni Peccati 氏 (Université du Luxembourg)
Stochastic geometry and Malliavin calculus on configuration spaces
[ 講演概要 ]
I will present some recent advances in the domain of quantitative limit theorems for geometric Poisson functionals, associated e.g. with random geometric graphs and random tessellations, obtained by means of Malliavin calculus techniques. One of our main results consists in a general (optimal) Berry-Esseen bound for stabilizing functionals, based on Stein’s method, iterated Poincaré inequalities and a variant of Mehler’s formula. Based on several joint works with S. Bourguin, R. Lachièze-Rey, G. Last and M. Schulte, as well as on the recent monograph that I co-edited with M. Reitzner.

### 2016年10月28日(金)

#### 数理人口学・数理生物学セミナー

13:30-14:30   数理科学研究科棟(駒場) 126号室

When is the allergen immunotherapy effective? (JAPANESE)
[ 講演概要 ]
Allergen immunotherapy is a method to treat allergic symptoms, for example rhinitis and sneezing in Japanese cedar pollen allergy (JCPA). In the immunotherapy of JCPA, patients take in a small amount of pollen over several years, which suppress severe allergic symptoms when exposed to a large amount of environmental pollen after the therapy. We develop a simple mathematical model to identify the condition for successful therapy. We consider the dynamics of type 2 T helper cells (Th2) and regulatory T cells (Treg) and both of them are differentiated from naive T cells. We assume that Treg cells have a much longer lifespan than Th2 cells, which makes Treg cells accumulate over many years during the therapy.
We regard that the therapy is successful if (1) without therapy the patient develops allergic symptoms upon exposure to the environmental pollen, (2) the patient does not develop allergic symptoms caused by the therapy itself, and (3) with therapy the patient does not develop symptoms upon exposure. We find the conditions of each parameter for successful therapy. We also find that the therapy of linearly increasing dose is able to reduce the risk of allergic symptoms caused by the therapy itself, rather than constant dose. We would like to consider application of this model to other kind of allergy, such as food allergy.