## 過去の記録

過去の記録 ～02/23｜本日 02/24 | 今後の予定 02/25～

### 2016年08月29日(月)

#### PDE実解析研究会

10:30-11:30 数理科学研究科棟(駒場) 268号室

通常の開催曜日、会場と異なります。

The Navier-Stokes equations: stationary existence, conditional regularity, and self-similar singularities (English)

https://www.math.lsu.edu/~pcnguyen/

通常の開催曜日、会場と異なります。

**Nguyen Cong Phuc 氏**(Louisiana State University)The Navier-Stokes equations: stationary existence, conditional regularity, and self-similar singularities (English)

[ 講演概要 ]

In this talk, both stationary and time-dependent Navier-Stokes equations are discussed. The common theme is that the quadratic nonlinearity and the pressure are both treated as weights generally belonging to a Sobolev space of negative order. We obtain the unique existence of solutions to stationary Navier-Stokes equations with small singular external forces that belong to a critical space. This result can be viewed as the stationary counterpart of an existence result obtained by H. Koch and D. Tataru for the free non-stationary Navier-Stokes equations with small initial data in $BMO^{-1}$. In another direction, some new local energy bounds are obtained for the time-dependent Navier-Stokes equations which imply the regularity condition $L_{t}^{\infty}(X)$, where $X$ is a non-endpoint borderline Lorentz space $X=L_{x}^{3, q}, q\not=\infty$. The analysis also allows us to rule out the existence of Leray's backward self-similar solutions to the Navier–Stokes equations with profiles in $L^{12/5}(\mathbb{R}^3)$ or in the Marcinkiewicz space $L^{q, \infty}(\mathbb{R}^{3})$ for any $q \in (12/5, 6)$.

This talk is based on joint work with Tuoc Van Phan and Cristi Guevara.

[ 講演参考URL ]In this talk, both stationary and time-dependent Navier-Stokes equations are discussed. The common theme is that the quadratic nonlinearity and the pressure are both treated as weights generally belonging to a Sobolev space of negative order. We obtain the unique existence of solutions to stationary Navier-Stokes equations with small singular external forces that belong to a critical space. This result can be viewed as the stationary counterpart of an existence result obtained by H. Koch and D. Tataru for the free non-stationary Navier-Stokes equations with small initial data in $BMO^{-1}$. In another direction, some new local energy bounds are obtained for the time-dependent Navier-Stokes equations which imply the regularity condition $L_{t}^{\infty}(X)$, where $X$ is a non-endpoint borderline Lorentz space $X=L_{x}^{3, q}, q\not=\infty$. The analysis also allows us to rule out the existence of Leray's backward self-similar solutions to the Navier–Stokes equations with profiles in $L^{12/5}(\mathbb{R}^3)$ or in the Marcinkiewicz space $L^{q, \infty}(\mathbb{R}^{3})$ for any $q \in (12/5, 6)$.

This talk is based on joint work with Tuoc Van Phan and Cristi Guevara.

https://www.math.lsu.edu/~pcnguyen/

### 2016年08月12日(金)

#### FMSPレクチャーズ

15:00-16:00 数理科学研究科棟(駒場) 128号室

Multiscale simulations of waves and applications (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Chung.pdf

**Eric Chung 氏**(Chinese Univ. of Hong Kong)Multiscale simulations of waves and applications (ENGLISH)

[ 講演概要 ]

Numerical simulations of wave propagation in heterogeneous media are important in many applications such as seismic propagation and seismic inversion.

In this talk, we will present a new multiscale approach for seismic wave propagation.

The method is able to compute the solution with much fewer degrees of freedom compared with fine mesh simulation.

The idea is to capture the multiscale features of the solutions by carefully designed multiscale basis functions.

We will also present applications to inverse problems.

[ 講演参考URL ]Numerical simulations of wave propagation in heterogeneous media are important in many applications such as seismic propagation and seismic inversion.

In this talk, we will present a new multiscale approach for seismic wave propagation.

The method is able to compute the solution with much fewer degrees of freedom compared with fine mesh simulation.

The idea is to capture the multiscale features of the solutions by carefully designed multiscale basis functions.

We will also present applications to inverse problems.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Chung.pdf

#### FMSPレクチャーズ

16:00-17:00 数理科学研究科棟(駒場) 128号室

Discrete regularization of parameter identification problems (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Clason.pdf

**Christian Clason 氏**(University Duisburg-Essen)Discrete regularization of parameter identification problems (ENGLISH)

[ 講演概要 ]

This talk is concerned with parameter identification problems where a distributed parameter is known a priori to take on values from a given set. This property can be promoted with the aid of a convex regularization term in the Tikhonov functional. We discuss the properties of minimizers of this functional and their numerical computation using a semismooth Newton method.

[ 講演参考URL ]This talk is concerned with parameter identification problems where a distributed parameter is known a priori to take on values from a given set. This property can be promoted with the aid of a convex regularization term in the Tikhonov functional. We discuss the properties of minimizers of this functional and their numerical computation using a semismooth Newton method.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Clason.pdf

### 2016年08月10日(水)

#### FMSPレクチャーズ

10:00-11:00 数理科学研究科棟(駒場) 370号室

Global-local-integration-based kernel approximation methods: Technical arguments (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon2.pdf

**Benny Y C Hon 氏**(City Univ. of Hong Kong)Global-local-integration-based kernel approximation methods: Technical arguments (ENGLISH)

[ 講演概要 ]

We discuss technical details of my talk on 8 Aug. and give also proofs of some main results.

[ 講演参考URL ]We discuss technical details of my talk on 8 Aug. and give also proofs of some main results.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon2.pdf

#### 統計数学セミナー

13:00-14:30 数理科学研究科棟(駒場) 117号室

Malliavin calculus and normal approximations

**David Nualart 氏**(Kansas University)Malliavin calculus and normal approximations

### 2016年08月09日(火)

#### 統計数学セミナー

13:00-16:30 数理科学研究科棟(駒場) 117号室

本ワークショップ・レクチャーは統計数学セミナー共催であり，JST CRESTによってサポートされています.

Malliavin calculus and normal approximations

http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=180

本ワークショップ・レクチャーは統計数学セミナー共催であり，JST CRESTによってサポートされています.

**David Nualart 氏**(Kansas University)Malliavin calculus and normal approximations

[ 講演概要 ]

The purpose of these lectures is to introduce some recent results on the application of Malliavin calculus combined with Stein's method to normal approximation. The Malliavin calculus is a differential calculus on the Wiener space. First, we will present some elements of Malliavin calculus, defining the basic differential operators: the derivative, its adjoint called the divergence operator and the generator of the Ornstein-Uhlenbeck semigroup. The behavior of these operators on the Wiener chaos expansion will be discussed. Then, we will introduce the Stein's method for normal approximation, which leads to general bounds for the Kolmogorov and total variation distances between the law of a Brownian functional and the standard normal distribution. In this context, the integration by parts formula of Malliavin calculus will allow us to express these bounds in terms of the Malliavin operators. We will present the application of this methodology to derive the Fourth Moment Theorem for a sequence of multiple stochastic integrals, and we will discuss some results on the uniform convergence of densities obtained using Malliavin calculus techniques. Finally, examples of functionals of Gaussian processes, such as the fractional Brownian motion, will be discussed.

[ 講演参考URL ]The purpose of these lectures is to introduce some recent results on the application of Malliavin calculus combined with Stein's method to normal approximation. The Malliavin calculus is a differential calculus on the Wiener space. First, we will present some elements of Malliavin calculus, defining the basic differential operators: the derivative, its adjoint called the divergence operator and the generator of the Ornstein-Uhlenbeck semigroup. The behavior of these operators on the Wiener chaos expansion will be discussed. Then, we will introduce the Stein's method for normal approximation, which leads to general bounds for the Kolmogorov and total variation distances between the law of a Brownian functional and the standard normal distribution. In this context, the integration by parts formula of Malliavin calculus will allow us to express these bounds in terms of the Malliavin operators. We will present the application of this methodology to derive the Fourth Moment Theorem for a sequence of multiple stochastic integrals, and we will discuss some results on the uniform convergence of densities obtained using Malliavin calculus techniques. Finally, examples of functionals of Gaussian processes, such as the fractional Brownian motion, will be discussed.

http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=180

### 2016年08月08日(月)

#### FMSPレクチャーズ

16:30-17:30 数理科学研究科棟(駒場) 128号室

Global-local-integration-based kernel approximation methods (ENGLISH)

[ 講演参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon.pdf

**Benny Y C Hon 氏**(City Univ. of Hong Kong)Global-local-integration-based kernel approximation methods (ENGLISH)

[ 講演参考URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hon.pdf

#### FMSPレクチャーズ

17:30-18:30 数理科学研究科棟(駒場) 128号室

On the lifting of deterministic convergence results for inverse problems to the stochastic setting (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gerth.pdf

**Daniel Gerth 氏**(Tech. Univ. Chemnitz)On the lifting of deterministic convergence results for inverse problems to the stochastic setting (ENGLISH)

[ 講演概要 ]

In inverse problems, the inevitable measurement noise is modelled either by a deterministic worst-case model or a stochastic one.

The development of convergence theory in both approaches appears to be rather disconnected. In this talk we seek to bridge this gap and show how deterministic result can be transferred into the stochastic setting. The talk is split into two parts. In the first part, after briefly introducing "inverse problems" and the noise models, we examine the particular problem of sparsity-promoting regularization with a Besov-space penalty term to demonstrate the lifting technique. In the second part, we present a generalization of the technique that applies to a large group of regularization methods.

[ 講演参考URL ]In inverse problems, the inevitable measurement noise is modelled either by a deterministic worst-case model or a stochastic one.

The development of convergence theory in both approaches appears to be rather disconnected. In this talk we seek to bridge this gap and show how deterministic result can be transferred into the stochastic setting. The talk is split into two parts. In the first part, after briefly introducing "inverse problems" and the noise models, we examine the particular problem of sparsity-promoting regularization with a Besov-space penalty term to demonstrate the lifting technique. In the second part, we present a generalization of the technique that applies to a large group of regularization methods.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Gerth.pdf

### 2016年08月06日(土)

#### 統計数学セミナー

10:00-17:10 数理科学研究科棟(駒場) 123号室

本ワークショップ・レクチャーは統計数学セミナー共催であり，JST CRESTによってサポートされています．

Asymptotic expansion of variations

LAMN property and optimal estimation for diffusion with non synchronous observations

Approximation schemes for stochastic differential equations driven by a fractional Brownian motion

Parameter estimation for fractional Ornstein-Uhlenbeck processes

Stein's equations for invariant measures of diffusions processes and their applications via Malliavin calculus

Asymptotic expansion of a nonlinear oscillator with a jump diffusion

[ 講演参考URL ]

http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=179

本ワークショップ・レクチャーは統計数学セミナー共催であり，JST CRESTによってサポートされています．

**Nakahiro Yoshida 氏**(University of Tokyo, Institute of Statistical Mathematics, and JST CREST) 10:00-10:50Asymptotic expansion of variations

**Teppei Ogihara 氏**(The Institute of Statistical Mathematics, JST PRESTO, and JST CREST) 11:00-11:50LAMN property and optimal estimation for diffusion with non synchronous observations

**David Nualart 氏**(Kansas University) 13:10-14:00Approximation schemes for stochastic differential equations driven by a fractional Brownian motion

**David Nualart 氏**(Kansas University) 14:10-15:00Parameter estimation for fractional Ornstein-Uhlenbeck processes

**Seiichiro Kusuoka 氏**(Okayama University) 15:20-16:10Stein's equations for invariant measures of diffusions processes and their applications via Malliavin calculus

**Yasushi Ishikawa 氏**(Ehime University) 16:20-17:10Asymptotic expansion of a nonlinear oscillator with a jump diffusion

[ 講演参考URL ]

http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=179

### 2016年07月28日(木)

#### 博士論文発表会

15:00-16:15 数理科学研究科棟(駒場) 118号室

Calabi-Yau 3-folds in Grassmannians and their I-functions （グラスマン多様体に含まれる3 次元カラビ・ヤウ多様体とそれらのI-関数）

(JAPANESE)

**井上 大輔 氏**(東京大学大学院数理科学研究科)Calabi-Yau 3-folds in Grassmannians and their I-functions （グラスマン多様体に含まれる3 次元カラビ・ヤウ多様体とそれらのI-関数）

(JAPANESE)

### 2016年07月27日(水)

#### 数理人口学・数理生物学セミナー

15:00-16:00 数理科学研究科棟(駒場) 128号室

The ecological dynamics of non-polio enteroviruses: Case studies from China and Japan (ENGLISH)

**Saki Takahashi 氏**(Princeton University)The ecological dynamics of non-polio enteroviruses: Case studies from China and Japan (ENGLISH)

[ 講演概要 ]

As we approach global eradication of poliovirus (Enterovirus C species), its relatives are rapidly emerging as public health threats. One of these viruses, Enterovirus A71 (EV-A71), has been implicated in large outbreaks of hand, foot, and mouth disease (HFMD), a childhood illness that has had a substantial burden throughout East and Southeast Asia over the past fifteen years. HFMD is typically a self-limiting disease, but a small proportion of EV-A71 infections lead to the development of neurological and systemic complications that can be fatal. EV-A71 also exhibits puzzling spatial characteristics: the virus circulates at low levels worldwide, but has so far been endemic and associated with severe disease exclusively in Asia. In this talk, I will present findings from a recent study that we did to characterize the transmission dynamics of HFMD in China, where over one million cases are reported each year. I will then describe recent efforts to explain the observed multi-annual cyclicity of EV-A71 incidence in Japan and to probe the contributions of other serotypes to the observed burden of HFMD. In closing, I will discuss plans for unifying data and modeling to study this heterogeneity in the endemicity of EV-A71, as well as to broadly better understand the spatial and viral dynamics of this group of infections.

As we approach global eradication of poliovirus (Enterovirus C species), its relatives are rapidly emerging as public health threats. One of these viruses, Enterovirus A71 (EV-A71), has been implicated in large outbreaks of hand, foot, and mouth disease (HFMD), a childhood illness that has had a substantial burden throughout East and Southeast Asia over the past fifteen years. HFMD is typically a self-limiting disease, but a small proportion of EV-A71 infections lead to the development of neurological and systemic complications that can be fatal. EV-A71 also exhibits puzzling spatial characteristics: the virus circulates at low levels worldwide, but has so far been endemic and associated with severe disease exclusively in Asia. In this talk, I will present findings from a recent study that we did to characterize the transmission dynamics of HFMD in China, where over one million cases are reported each year. I will then describe recent efforts to explain the observed multi-annual cyclicity of EV-A71 incidence in Japan and to probe the contributions of other serotypes to the observed burden of HFMD. In closing, I will discuss plans for unifying data and modeling to study this heterogeneity in the endemicity of EV-A71, as well as to broadly better understand the spatial and viral dynamics of this group of infections.

### 2016年07月26日(火)

#### 統計数学セミナー

13:00-14:30 数理科学研究科棟(駒場) 052号室

本講演は大阪大学で行い，東京大学へWeb配信いたします.

Multilevel Particle Filters

本講演は大阪大学で行い，東京大学へWeb配信いたします.

**Ajay Jasra 氏**(National University of Singapore)Multilevel Particle Filters

[ 講演概要 ]

In this talk the filtering of partially observed diffusions,

with discrete-time observations, is considered.

It is assumed that only biased approximations of the diffusion can be

obtained, for choice of an accuracy parameter indexed by $l$.

A multilevel estimator is proposed, consisting of a telescopic sum of

increment estimators associated to the successive levels.

The work associated to $\cO(\varepsilon^2)$ mean-square error between

the multilevel estimator and average with respect to the filtering

distribution is shown to scale optimally, for example as

$\cO(\varepsilon^{-2})$ for optimal rates of convergence of the

underlying diffusion approximation.

The method is illustrated on several examples.

In this talk the filtering of partially observed diffusions,

with discrete-time observations, is considered.

It is assumed that only biased approximations of the diffusion can be

obtained, for choice of an accuracy parameter indexed by $l$.

A multilevel estimator is proposed, consisting of a telescopic sum of

increment estimators associated to the successive levels.

The work associated to $\cO(\varepsilon^2)$ mean-square error between

the multilevel estimator and average with respect to the filtering

distribution is shown to scale optimally, for example as

$\cO(\varepsilon^{-2})$ for optimal rates of convergence of the

underlying diffusion approximation.

The method is illustrated on several examples.

### 2016年07月25日(月)

#### 代数幾何学セミナー

13:30-15:00 数理科学研究科棟(駒場) 122号室

今週は月曜日にセミナーがあります。また13:30--15:00と15:30--17:00に二つの講演があります。This week's seminar will be held on Monday, and we have two seminars from 13:30--15:00 and from 15:30--17:00.

Birational rigidity of complete intersections (English)

今週は月曜日にセミナーがあります。また13:30--15:00と15:30--17:00に二つの講演があります。This week's seminar will be held on Monday, and we have two seminars from 13:30--15:00 and from 15:30--17:00.

**鈴木文顕 氏**(東大数理)Birational rigidity of complete intersections (English)

[ 講演概要 ]

A complete intersection defined by s hypersurfaces of degree d_1, ... ,d_s in a projective space P^N is Q-Fano, i.e. normal, Q-factorial, terminal and having an ample anti-canonical divisor, if d_1 + ... + d_s is at most N and it has only mild singularities. Then it is rationally-connected by the results of Kollar-Miyaoka-Mori, Zhang and Hacon-Mckernan. A natural question is to determine its rationality. If its dimension or degree is at most 2, then it is rational. How about the remaining cases?

When d_1 + ... + d_s = N, birational rigidity give one of the most effective ways to tackle this problem. We recall that a Q-Fano variety is birationally superrigid if any birational map to the source of another Mori fiber space is isomorphism. It implies that X is non-rational and Bir(X) = Aut(X). After the works of Iskovskih-Manin, Pukhlikov, Chelt'so and de Fernex-Ein-Mustata, de Fernex proved that every smooth hypersurface of degree N in P^N is birationally superrigid for N at least 4. He also proved birational superrigidity of a large class of singular hypersurfaces of this type.

In this talk, we would like to extend de Fernex's results to complete intersections. As a key step, we generalize Pukhlikov's multiplicity bounds of cycles in hypersurfaces to complete intersections.

A complete intersection defined by s hypersurfaces of degree d_1, ... ,d_s in a projective space P^N is Q-Fano, i.e. normal, Q-factorial, terminal and having an ample anti-canonical divisor, if d_1 + ... + d_s is at most N and it has only mild singularities. Then it is rationally-connected by the results of Kollar-Miyaoka-Mori, Zhang and Hacon-Mckernan. A natural question is to determine its rationality. If its dimension or degree is at most 2, then it is rational. How about the remaining cases?

When d_1 + ... + d_s = N, birational rigidity give one of the most effective ways to tackle this problem. We recall that a Q-Fano variety is birationally superrigid if any birational map to the source of another Mori fiber space is isomorphism. It implies that X is non-rational and Bir(X) = Aut(X). After the works of Iskovskih-Manin, Pukhlikov, Chelt'so and de Fernex-Ein-Mustata, de Fernex proved that every smooth hypersurface of degree N in P^N is birationally superrigid for N at least 4. He also proved birational superrigidity of a large class of singular hypersurfaces of this type.

In this talk, we would like to extend de Fernex's results to complete intersections. As a key step, we generalize Pukhlikov's multiplicity bounds of cycles in hypersurfaces to complete intersections.

#### 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

Intermittent property of parabolic stochastic partial differential equations

**謝 賓 氏**(信州大学理学部数学科)Intermittent property of parabolic stochastic partial differential equations

#### 代数幾何学セミナー

15:30-17:00 数理科学研究科棟(駒場) 122号室

今週は月曜日にセミナーがあります。また13:30--15:00と15:30--17:00に二つの講演があります。This week's seminar will be held on Monday, and we have two seminars from 13:30--15:00 and from 15:30--17:00.

On the geometry of thin exceptional sets in Manin’s conjecture

今週は月曜日にセミナーがあります。また13:30--15:00と15:30--17:00に二つの講演があります。This week's seminar will be held on Monday, and we have two seminars from 13:30--15:00 and from 15:30--17:00.

**谷本 祥 氏**(University of Copenhagen)On the geometry of thin exceptional sets in Manin’s conjecture

[ 講演概要 ]

Manin’s conjecture predicts the asymptotic formula for the counting function of rational points on a Fano variety X after removing the exceptional sets. The original conjecture, which removes a proper closed subset, is wrong due to covering families of subvarieties violating the compatibility of Manin’s conjecture, and its refinement, suggested by Emmanuel Peyre, removes a thin set instead of a closed set. In this talk, first I would like to explain that subvarieties which conjecturally have more points than X only form a thin set using the minimal model program and the boundedness of log Fano varieties. After that, I would like to discuss our conjecture on the birational boundedness of covers violating the compatibility of Manin’s conjecture, and present some results in dimension 2 and 3. This is joint work with Brian Lehmann.

Manin’s conjecture predicts the asymptotic formula for the counting function of rational points on a Fano variety X after removing the exceptional sets. The original conjecture, which removes a proper closed subset, is wrong due to covering families of subvarieties violating the compatibility of Manin’s conjecture, and its refinement, suggested by Emmanuel Peyre, removes a thin set instead of a closed set. In this talk, first I would like to explain that subvarieties which conjecturally have more points than X only form a thin set using the minimal model program and the boundedness of log Fano varieties. After that, I would like to discuss our conjecture on the birational boundedness of covers violating the compatibility of Manin’s conjecture, and present some results in dimension 2 and 3. This is joint work with Brian Lehmann.

### 2016年07月22日(金)

#### 作用素環セミナー

16:45-18:15 数理科学研究科棟(駒場) 118号室

Radius of comparison for $C^*$ crossed products by free minimal actions of amenable groups

**N. Christopher Phillips 氏**(Univ. Oregon)Radius of comparison for $C^*$ crossed products by free minimal actions of amenable groups

### 2016年07月19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

The geometry of the curve graphs and beyond (JAPANESE)

Tea: Common Room 16:30-17:00

**渡邊 陽介 氏**(University of Hawaii)The geometry of the curve graphs and beyond (JAPANESE)

[ 講演概要 ]

The curve graphs are locally infinite. However, by using Masur-Minsky's tight geodesics, one could view them as locally finite graphs. Bell-Fujiwara used a special property of tight geodesics and showed that the asymptotic dimension of the curve graphs is finite. In this talk, I will introduce a new class of geodesics which also has the property. If time permits, I will explain how such geodesics can be adapted in Out(F_n) setting.

The curve graphs are locally infinite. However, by using Masur-Minsky's tight geodesics, one could view them as locally finite graphs. Bell-Fujiwara used a special property of tight geodesics and showed that the asymptotic dimension of the curve graphs is finite. In this talk, I will introduce a new class of geodesics which also has the property. If time permits, I will explain how such geodesics can be adapted in Out(F_n) setting.

#### 博士論文発表会

13:00-14:15 数理科学研究科棟(駒場) 126号室

Cube invariance of higher Chow groups with modulus （モジュラス付き高次チャウ群のキューブ不変性)

(JAPANESE)

**宮﨑 弘安 氏**(東京大学大学院数理科学研究科)Cube invariance of higher Chow groups with modulus （モジュラス付き高次チャウ群のキューブ不変性)

(JAPANESE)

### 2016年07月13日(水)

#### 社会数理コロキウム

17:00-18:30 数理科学研究科棟(駒場) 002号室

講演終了後2階コモンルームで情報交換会を行います。

企業での研究開発の取り組み～数学を使った情報理論、人工知能の研究紹介～ (JAPANESE)

http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20160713.pdf

講演終了後2階コモンルームで情報交換会を行います。

**伊東 利雄 氏**(富士通研究所)企業での研究開発の取り組み～数学を使った情報理論、人工知能の研究紹介～ (JAPANESE)

[ 講演概要 ]

情報理論と人工知能の分野の中に、符号理論、圧縮センシング、ニューラルネットワーク

などの技術があり、ガロア体、代数曲線、確率を用いた尤度推定、多様体、L^1ノルム

正則化、微分方程式など様々な数学が用いられています。またこれらの技術はハードディスクや

携帯電話にも応用されています。本講演では、これらの技術から自分が取り組んできた研究に

ついていくつかをご紹介したいと思います。またニューラルネットワークの研究について、

脳神経科学との関わりについても少し触れてみたいと思います。

[ 講演参考URL ]情報理論と人工知能の分野の中に、符号理論、圧縮センシング、ニューラルネットワーク

などの技術があり、ガロア体、代数曲線、確率を用いた尤度推定、多様体、L^1ノルム

正則化、微分方程式など様々な数学が用いられています。またこれらの技術はハードディスクや

携帯電話にも応用されています。本講演では、これらの技術から自分が取り組んできた研究に

ついていくつかをご紹介したいと思います。またニューラルネットワークの研究について、

脳神経科学との関わりについても少し触れてみたいと思います。

http://fmsp.ms.u-tokyo.ac.jp/FMSP_colloquium20160713.pdf

#### 数理人口学・数理生物学セミナー

15:00-16:00 数理科学研究科棟(駒場) 128演習室号室

腫瘍免疫系における時間遅れの二元的な役割 (ENGLISH)

**Yu Min 氏**(青山学院大学理工学部)腫瘍免疫系における時間遅れの二元的な役割 (ENGLISH)

[ 講演概要 ]

In this talk, a previous tumor immune interaction model is simplified by considering a relatively weak immune activation, which can still keep the essential dynamics properties. Since the immune activation process is not instantaneous, we incorporate one delay effect for the activation of the effector cells by helper T cells into the model. Furthermore, we investigate the stability and instability region of the tumor-presence equilibrium state of the delay-induced system with respect to two parameters, the activation rate of effector cells by helper T cells and the helper T cells stimulation rate by the presence of identified tumor antigens. We show the dual role of this delay that can induce stability switches exhibiting destabilization as well as stabilization of the tumor-presence equilibrium. Besides, our results show that the appropriate immune activation time plays a significant role in control of tumor growth.

In this talk, a previous tumor immune interaction model is simplified by considering a relatively weak immune activation, which can still keep the essential dynamics properties. Since the immune activation process is not instantaneous, we incorporate one delay effect for the activation of the effector cells by helper T cells into the model. Furthermore, we investigate the stability and instability region of the tumor-presence equilibrium state of the delay-induced system with respect to two parameters, the activation rate of effector cells by helper T cells and the helper T cells stimulation rate by the presence of identified tumor antigens. We show the dual role of this delay that can induce stability switches exhibiting destabilization as well as stabilization of the tumor-presence equilibrium. Besides, our results show that the appropriate immune activation time plays a significant role in control of tumor growth.

### 2016年07月12日(火)

#### 代数幾何学セミナー

15:30-17:00 数理科学研究科棟(駒場) 122号室

同じ日の13:30--15:00, 126室で、同講師による標数0の特異点解消の講義があります. We have a complimentary lecture by Matsuki-sensei on the resolution in characteristic 0 (from 13:30-15:00 at room#126).

Hypersurfaces of maximal contact and jumping phenomenon in the problem of resolution of singularities in positive characteristic (English)

https://www.math.purdue.edu/people/bio/kmatsuki/home

同じ日の13:30--15:00, 126室で、同講師による標数0の特異点解消の講義があります. We have a complimentary lecture by Matsuki-sensei on the resolution in characteristic 0 (from 13:30-15:00 at room#126).

**Kenji Matsuki 氏**(Purdue/RIMS)Hypersurfaces of maximal contact and jumping phenomenon in the problem of resolution of singularities in positive characteristic (English)

[ 講演概要 ]

According to our approach for resolution of singularities in positive characteristic (called the Idealistic Filtration Program, alias the I.F.P.) the algorithm is divided into the following two steps:

Step 1. Reduction of the general case to the monomial case.

Step 2. Solution in the monomial case.

While we have established Step 1 in abritrary dimension, Step 2 becomes very subtle and difficult in positive characteristic. This is in clear contrast to the classical setting in characteristic zero, where the solution in the monomial case is quite easy.

The talk consists of the two parts.

・Part I [13:30--15:00]: This part is mainly for the students, who are not familiar with the classical results in characteristic zero. Through Hironaka's reformulation of the problem of resolution of singularities, we will see how the notion of a hypersurface of maximal contact provides an inductive structure on dimension to the problem, and hence leading to a solution. Since our I.F.P. is closely modelled upon the classical algorithm in characteristic zero, this part should also give some background material and motivation for our approach in positive characteristic.

in

・Part II [15:30--17:00]: This is the main body of my talk. I will proceed according to the following menu.

{\bf Framewrok of the I.F.P.}: First I will explain the framewrok of the I.F.P., which further extends Hironaka's refomulation. The biggest obstacle to establish Step 1 is the fact that, in positive characteristic, a smooth hypersurface of maximal contact does not exist in general. In order to overcome this obstacle, we introduce the notion of the Leading Generator System, which is the collection of multiple singular hypersurfaces of maximal contcat.

{\bf Monomial Case}: As metioned above, then the problem is reduced to the one in the monomial case.

・ {\bf Inductive scheme on the invariant \boldmath$\tau$}: We firstly observe that, by the inductive scheme on the invariant $\tau$, we have only to consider the case with $\tau = 1$, i.e., the case where there is only one single singular hypersurface of maximal contact.

・ {\bf Tight Monomail Case}: We secondly observe that, if we reach the so-called Tight Monomial Case, then we can easily solve the problem.

・ {\bf Introduction of the invariant `` \boldmath$\mathrm{inv}_{\mathrm{MON},real}$''}: Thus our final task is, after arriving at the monimial case with $\tau = 1$, to reach the Tight Monomial Case, which is characterized by $\mathrm{inv}_{\mathrm{MON},real} = 0$.

・ {\bf Moh-Hauser Jumping phenomenon}: The invariant $\mathrm{inv}_{\mathrm{MON},real}$ usually behaves well, i.e., decreases after each blow up. But under some circustances, it strictly increases. I will explain this well-known Moh-Jumping phenomenon by giving a simple example.

・ {\bf Eventual decrease of the jumping peaks}: At last, the problem boils down to analyzing and overcoming the Moh-Hauser Jumping phenomenon. For this purpose, we will present the conjecture of ``Eventual decrease of the jumping peaks'', which is affirmatively solved in dimension 3, and is the current focus of our research in dimension 4.

[ 講演参考URL ]According to our approach for resolution of singularities in positive characteristic (called the Idealistic Filtration Program, alias the I.F.P.) the algorithm is divided into the following two steps:

Step 1. Reduction of the general case to the monomial case.

Step 2. Solution in the monomial case.

While we have established Step 1 in abritrary dimension, Step 2 becomes very subtle and difficult in positive characteristic. This is in clear contrast to the classical setting in characteristic zero, where the solution in the monomial case is quite easy.

The talk consists of the two parts.

・Part I [13:30--15:00]: This part is mainly for the students, who are not familiar with the classical results in characteristic zero. Through Hironaka's reformulation of the problem of resolution of singularities, we will see how the notion of a hypersurface of maximal contact provides an inductive structure on dimension to the problem, and hence leading to a solution. Since our I.F.P. is closely modelled upon the classical algorithm in characteristic zero, this part should also give some background material and motivation for our approach in positive characteristic.

in

・Part II [15:30--17:00]: This is the main body of my talk. I will proceed according to the following menu.

{\bf Framewrok of the I.F.P.}: First I will explain the framewrok of the I.F.P., which further extends Hironaka's refomulation. The biggest obstacle to establish Step 1 is the fact that, in positive characteristic, a smooth hypersurface of maximal contact does not exist in general. In order to overcome this obstacle, we introduce the notion of the Leading Generator System, which is the collection of multiple singular hypersurfaces of maximal contcat.

{\bf Monomial Case}: As metioned above, then the problem is reduced to the one in the monomial case.

・ {\bf Inductive scheme on the invariant \boldmath$\tau$}: We firstly observe that, by the inductive scheme on the invariant $\tau$, we have only to consider the case with $\tau = 1$, i.e., the case where there is only one single singular hypersurface of maximal contact.

・ {\bf Tight Monomail Case}: We secondly observe that, if we reach the so-called Tight Monomial Case, then we can easily solve the problem.

・ {\bf Introduction of the invariant `` \boldmath$\mathrm{inv}_{\mathrm{MON},real}$''}: Thus our final task is, after arriving at the monimial case with $\tau = 1$, to reach the Tight Monomial Case, which is characterized by $\mathrm{inv}_{\mathrm{MON},real} = 0$.

・ {\bf Moh-Hauser Jumping phenomenon}: The invariant $\mathrm{inv}_{\mathrm{MON},real}$ usually behaves well, i.e., decreases after each blow up. But under some circustances, it strictly increases. I will explain this well-known Moh-Jumping phenomenon by giving a simple example.

・ {\bf Eventual decrease of the jumping peaks}: At last, the problem boils down to analyzing and overcoming the Moh-Hauser Jumping phenomenon. For this purpose, we will present the conjecture of ``Eventual decrease of the jumping peaks'', which is affirmatively solved in dimension 3, and is the current focus of our research in dimension 4.

https://www.math.purdue.edu/people/bio/kmatsuki/home

#### 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

Non-arithmetic lattices (ENGLISH)

Tea: Common Room 16:30-17:00

**John Parker 氏**(Durham University)Non-arithmetic lattices (ENGLISH)

[ 講演概要 ]

In this talk I will discuss arithmetic and non-arithmetic lattices and I will give a history of the problem of finding non-arithmetic lattices. I will also briefly describe the construction of new non-arithmetic lattices in SU(2,1) found in my joint workwith Martin Deraux and Julien Paupert.

In this talk I will discuss arithmetic and non-arithmetic lattices and I will give a history of the problem of finding non-arithmetic lattices. I will also briefly describe the construction of new non-arithmetic lattices in SU(2,1) found in my joint workwith Martin Deraux and Julien Paupert.

#### PDE実解析研究会

10:20-11:00 数理科学研究科棟(駒場) 056号室

通常の開催時間と異なります。

Special cases of the planar least gradient problem (English)

通常の開催時間と異なります。

**Piotr Rybka 氏**(University of Warsaw)Special cases of the planar least gradient problem (English)

[ 講演概要 ]

We study the least gradient problem in two special cases:

(1) the natural boundary conditions are imposed on a part of the strictly convex domain while the Dirichlet data are given on the rest of the boundary; or

(2) the Dirichlet data are specified on the boundary of a rectangle. We show existence of solutions and study properties of solution for special cases of the data. We are particularly interested in uniqueness and continuity of solutions.

We study the least gradient problem in two special cases:

(1) the natural boundary conditions are imposed on a part of the strictly convex domain while the Dirichlet data are given on the rest of the boundary; or

(2) the Dirichlet data are specified on the boundary of a rectangle. We show existence of solutions and study properties of solution for special cases of the data. We are particularly interested in uniqueness and continuity of solutions.

#### PDE実解析研究会

14:20-15:00 数理科学研究科棟(駒場) 056号室

通常の開催時間と異なります。

Global Strong $L^p$ Well-Posedness of the 3D Primitive Equations (English)

通常の開催時間と異なります。

**Amru Hussein 氏**(TU Darmstadt)Global Strong $L^p$ Well-Posedness of the 3D Primitive Equations (English)

[ 講演概要 ]

Primitive Equations are considered to be a fundamental model for geophysical flows. Here, the $L^p$ theory for the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, is developed. This set of equations is globally strongly well-posed for arbitrary large initial data lying in certain interpolation spaces, which are explicitly characterized as subspaces of $H^2/p$, $p$, $1 < p < \infty$, satisfying certain boundary conditions. Thus, the general $L^p$ setting admits rougher data than the usual $L^2$ theory with initial data in $H^1$.

In this study, the linearized Stokes type problem plays a prominent role, and it turns out that it can be treated efficiently using perturbation methods for $H^\infty$-calculus.

Primitive Equations are considered to be a fundamental model for geophysical flows. Here, the $L^p$ theory for the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, is developed. This set of equations is globally strongly well-posed for arbitrary large initial data lying in certain interpolation spaces, which are explicitly characterized as subspaces of $H^2/p$, $p$, $1 < p < \infty$, satisfying certain boundary conditions. Thus, the general $L^p$ setting admits rougher data than the usual $L^2$ theory with initial data in $H^1$.

In this study, the linearized Stokes type problem plays a prominent role, and it turns out that it can be treated efficiently using perturbation methods for $H^\infty$-calculus.

#### 解析学火曜セミナー

16:50-18:20 数理科学研究科棟(駒場) 126号室

Gevrey estimates of the resolvent and sub-exponential time-decay (English)

**X. P. Wang 氏**(Université de Nantes, France)Gevrey estimates of the resolvent and sub-exponential time-decay (English)

[ 講演概要 ]

For a class of non-selfadjoint Schrodinger operators satisfying some weighted coercive condition, we prove that the resolvent satisfies the Gevrey estimates at the threshold. As applications, we show that the heat and Schrodinger semigroups decay sub-exponentially in appropriately weighted spaces. We also study compactly supported perturbations of this class of operators where zero may be an embedded eigenvalue.

For a class of non-selfadjoint Schrodinger operators satisfying some weighted coercive condition, we prove that the resolvent satisfies the Gevrey estimates at the threshold. As applications, we show that the heat and Schrodinger semigroups decay sub-exponentially in appropriately weighted spaces. We also study compactly supported perturbations of this class of operators where zero may be an embedded eigenvalue.

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