## Seminar information archive

Seminar information archive ～02/15｜Today's seminar 02/16 | Future seminars 02/17～

#### Seminar on Probability and Statistics

16:10-17:10 Room #123 (Graduate School of Math. Sci. Bldg.)

LAMN property and optimal estimation for diffusion with non synchronous observations

**Teppei Ogihara**(Institute of Statistical Mathematics, JST PRESTO, JST CREST)LAMN property and optimal estimation for diffusion with non synchronous observations

[ Abstract ]

We study so-called local asymptotic mixed normality (LAMN) property for a statistical model generated by nonsynchronously observed diffusion processes using a Malliavin calculus technique. The LAMN property of the statistical model induces an asymptotic minimal variance of estimation errors for any estimators of the parameter. We also construct an optimal estimator which attains the best asymptotic variance.

We study so-called local asymptotic mixed normality (LAMN) property for a statistical model generated by nonsynchronously observed diffusion processes using a Malliavin calculus technique. The LAMN property of the statistical model induces an asymptotic minimal variance of estimation errors for any estimators of the parameter. We also construct an optimal estimator which attains the best asymptotic variance.

#### Seminar on Probability and Statistics

13:00-14:20 Room #123 (Graduate School of Math. Sci. Bldg.)

Stochastic heat equation with fractional noise 1

**Ciprian Tudor**(Université de Lille 1)Stochastic heat equation with fractional noise 1

[ Abstract ]

In the first part, we introduce the bifractional Brownian motion, which is a Gaussian process that generalizes the well- known fractional Brownian motion. We present the basic properties of this process and we also present its connection with the mild solution to the heat equation driven by a Gaussian noise that behaves as the Brownian motion in time.

In the first part, we introduce the bifractional Brownian motion, which is a Gaussian process that generalizes the well- known fractional Brownian motion. We present the basic properties of this process and we also present its connection with the mild solution to the heat equation driven by a Gaussian noise that behaves as the Brownian motion in time.

#### Seminar on Probability and Statistics

14:30-15:50 Room #123 (Graduate School of Math. Sci. Bldg.)

Stochastic heat equation with fractional noise 2

**Ciprian Tudor**(Université de Lille 1)Stochastic heat equation with fractional noise 2

[ Abstract ]

We will present recent result concerning the heat equation driven by q Gaussian noise which behaves as a fractional Brownian motion in time and has a correlated spatial structure. We give the basic results concerning the existence and the properties of the solution. We will also focus on the distribution of this Gaussian process and its connection with other fractional-type processes.

We will present recent result concerning the heat equation driven by q Gaussian noise which behaves as a fractional Brownian motion in time and has a correlated spatial structure. We give the basic results concerning the existence and the properties of the solution. We will also focus on the distribution of this Gaussian process and its connection with other fractional-type processes.

#### Mathematical Biology Seminar

15:00-16:00 Room #128演習室 (Graduate School of Math. Sci. Bldg.)

Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)

https://web.viu.ca/idelsl/

**Lev Idels**(Vanvouver Island University)Delayed Models of Cancer Dynamics: Lessons Learned in Mathematical Modelling (ENGLISH)

[ Abstract ]

In general, delay differential equations provide a richer mathematical

framework (compared with ordinary differential equations) for the

analysis of biosystems dynamics. The inclusion of explicit time lags in

tumor growth models allows direct reference to experimentally measurable

and/or controllable cell growth characteristics. For three different

types of angiogenesis models with variable delays, we consider either

continuous or impulse therapy that eradicates tumor cells and suppresses

angiogenesis. It was shown that with the growth of delays, even

constant, the equilibrium can lose its stability, and sustainable

oscillation, as well as chaotic behavior, can be observed. The analysis

outlines the difficulties which occur in the case of unbounded growth

rates, such as classical Gompertz model, for small volumes of cancer

cells compared to available blood vessels. The Wheldon model (1975) of a

Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of

recent discovery that this model has a major drawback.

[ Reference URL ]In general, delay differential equations provide a richer mathematical

framework (compared with ordinary differential equations) for the

analysis of biosystems dynamics. The inclusion of explicit time lags in

tumor growth models allows direct reference to experimentally measurable

and/or controllable cell growth characteristics. For three different

types of angiogenesis models with variable delays, we consider either

continuous or impulse therapy that eradicates tumor cells and suppresses

angiogenesis. It was shown that with the growth of delays, even

constant, the equilibrium can lose its stability, and sustainable

oscillation, as well as chaotic behavior, can be observed. The analysis

outlines the difficulties which occur in the case of unbounded growth

rates, such as classical Gompertz model, for small volumes of cancer

cells compared to available blood vessels. The Wheldon model (1975) of a

Chronic Myelogenous Leukemia (CML) dynamics is revisited in the light of

recent discovery that this model has a major drawback.

https://web.viu.ca/idelsl/

### 2016/04/25

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Graded twisting of quantum groups, actions, and categories

**Makoto Yamashita**(Ochanomizu Univ.)Graded twisting of quantum groups, actions, and categories

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The representative domain and its applications (JAPANESE)

**Atsushi Yamamori**(Academia Sinica)The representative domain and its applications (JAPANESE)

[ Abstract ]

Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.

Bergman introduced the notion of a representative domain to choose a nice holomorphic equivalence class of domains. In this talk, I will explain that the representative domain is also useful to obtain an analogue of Cartan's linearity theorem for some special class of domains.

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Concentration results for directed polymer with unbouded jumps

**Shuta Nakajima**(Research institute for mathematical sciences)Concentration results for directed polymer with unbouded jumps

### 2016/04/22

#### Seminar on Probability and Statistics

10:30-11:50 Room #002 (Graduate School of Math. Sci. Bldg.)

Stein method and Malliavin calculus : theory and some applications to limit theorems 1

**Ciprian Tudor**(Université de Lille 1)Stein method and Malliavin calculus : theory and some applications to limit theorems 1

[ Abstract ]

In this first part, we will present the basic ideas of the Stein method for the normal approximation. We will also describe its connection with the Malliavin calculus and the Fourth Moment Theorem.

In this first part, we will present the basic ideas of the Stein method for the normal approximation. We will also describe its connection with the Malliavin calculus and the Fourth Moment Theorem.

#### Seminar on Probability and Statistics

12:50-14:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Stein method and Malliavin calculus : theory and some applications to limit theorems 2

**Ciprian Tudor**(Université de Lille 1)Stein method and Malliavin calculus : theory and some applications to limit theorems 2

[ Abstract ]

In the second presentation, we intend to do the following: to illustrate the application of the Stein method to the limit behavior of the quadratic variation of Gaussian processes and its connection to statistics. We also intend to present the extension of the method to other target distributions.

In the second presentation, we intend to do the following: to illustrate the application of the Stein method to the limit behavior of the quadratic variation of Gaussian processes and its connection to statistics. We also intend to present the extension of the method to other target distributions.

#### Seminar on Probability and Statistics

14:20-15:50 Room #002 (Graduate School of Math. Sci. Bldg.)

Equivalence between the convergence in total variation and that of the Stein factor to the invariant measures of diffusion processes

**Seiichiro Kusuoka**(Okayama University)Equivalence between the convergence in total variation and that of the Stein factor to the invariant measures of diffusion processes

[ Abstract ]

We consider the characterization of the convergence of distributions to a given distribution in a certain class by using Stein's equation and Malliavin calculus with respect to the invariant measures of one-dimensional diffusion processes. Precisely speaking, we obtain an estimate between the so-called Stein factor and the total variation norm, and the equivalence between the convergence of the distributions in total variation and that of the Stein factor. This talk is based on the joint work with C.A.Tudor (arXiv:1310.3785).

We consider the characterization of the convergence of distributions to a given distribution in a certain class by using Stein's equation and Malliavin calculus with respect to the invariant measures of one-dimensional diffusion processes. Precisely speaking, we obtain an estimate between the so-called Stein factor and the total variation norm, and the equivalence between the convergence of the distributions in total variation and that of the Stein factor. This talk is based on the joint work with C.A.Tudor (arXiv:1310.3785).

#### Seminar on Probability and Statistics

16:10-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Asymptotic expansion and estimation of volatility

**Nakahiro Yoshida**(University of Tokyo, Institute of Statistical Mathematics, JST CREST)Asymptotic expansion and estimation of volatility

[ Abstract ]

Parametric estimation of volatility of an Ito process in a finite time horizon is discussed. Asymptotic expansion of the error distribution will be presented for the quasi likelihood estimators, i.e., quasi MLE, quasi Bayesian estimator and one-step quasi MLE. Statistics becomes non-ergodic, where the limit distribution is mixed normal. Asymptotic expansion is a basic tool in various areas in the traditional ergodic statistics such as higher order asymptotic decision theory, bootstrap and resampling plans, prediction theory, information criterion for model selection, information geometry, etc. Then a natural question is to obtain asymptotic expansion in the non-ergodic statistics. However, due to randomness of the characteristics of the limit, the classical martingale expansion or the mixing method cannot not apply. Recently a new martingale expansion was developed and applied to a quadratic form of the Ito process. The higher order terms are characterized by the adaptive random symbol and the anticipative random symbol. The Malliavin calculus is used for the description of the anticipative random symbols as well as for obtaining a decay of the characteristic functions. In this talk, the martingale expansion method and the quasi likelihood analysis with a polynomial type large deviation estimate of the quasi likelihood random field collaborate to derive expansions for the quasi likelihood estimators. Expansions of the realized volatility under microstructure noise, the power variation and the error of Euler-Maruyama scheme are recent applications. Further, some extension of martingale expansion to general martingales will be mentioned. References: SPA2013, arXiv:1212.5845, AISM2011, arXiv:1309.2071 (to appear in AAP), arXiv:1512.04716.

Parametric estimation of volatility of an Ito process in a finite time horizon is discussed. Asymptotic expansion of the error distribution will be presented for the quasi likelihood estimators, i.e., quasi MLE, quasi Bayesian estimator and one-step quasi MLE. Statistics becomes non-ergodic, where the limit distribution is mixed normal. Asymptotic expansion is a basic tool in various areas in the traditional ergodic statistics such as higher order asymptotic decision theory, bootstrap and resampling plans, prediction theory, information criterion for model selection, information geometry, etc. Then a natural question is to obtain asymptotic expansion in the non-ergodic statistics. However, due to randomness of the characteristics of the limit, the classical martingale expansion or the mixing method cannot not apply. Recently a new martingale expansion was developed and applied to a quadratic form of the Ito process. The higher order terms are characterized by the adaptive random symbol and the anticipative random symbol. The Malliavin calculus is used for the description of the anticipative random symbols as well as for obtaining a decay of the characteristic functions. In this talk, the martingale expansion method and the quasi likelihood analysis with a polynomial type large deviation estimate of the quasi likelihood random field collaborate to derive expansions for the quasi likelihood estimators. Expansions of the realized volatility under microstructure noise, the power variation and the error of Euler-Maruyama scheme are recent applications. Further, some extension of martingale expansion to general martingales will be mentioned. References: SPA2013, arXiv:1212.5845, AISM2011, arXiv:1309.2071 (to appear in AAP), arXiv:1512.04716.

### 2016/04/21

#### Geometry Colloquium

17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Spectral convergence under bounded Ricci curvature (Japanese)

**Shouhei Honda**(Tohoku University)Spectral convergence under bounded Ricci curvature (Japanese)

[ Abstract ]

For a noncollapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature, we establish two spectral convergence. One of them is on the Hodge Laplacian acting on differential one-forms. The other is on the connection Laplacian acting on tensor fields of every type, which include all differential forms. These are sharp generalizations of Cheeger-Colding's spectral convergence of the Laplacian acting on functions to the cases of tensor fields and differential forms. These spectral convergence have two direct corollaries. One of them is to give new bounds on such eigenvalues, in terms of bounds on volume, diameter and the Ricci curvature. The other is that we show the upper semicontinuity of the first Betti numbers with respect to the Gromov-Hausdorff topology, and give the equivalence between the continuity of them and the existence of a uniform spectral gap. On the other hand we also define measurable curvature tensors of the noncollapsed Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a uniform bound of Ricci curvature, which include Riemannian curvature tensor, the Ricci curvature, and the scalar curvature. As fundamental properties of our Ricci curvature, we show that the Ricci curvature coincides with the difference between the Hodge Laplacian and the connection Laplacian, and is compatible with Gigli's one and Lott's Ricci measure. Moreover we prove a lower bound of the Ricci curvature is compatible with a reduced Riemannian curvature dimension condition. We also give a positive answer to Lott's question on the behavior of the scalar curvature with respect to the Gromov-Hausdorff topology by using our scalar curvature. This talk is based on arXiv:1510.05349.

For a noncollapsed Gromov-Hausdorff convergent sequence of Riemannian manifolds with a uniform bound of Ricci curvature, we establish two spectral convergence. One of them is on the Hodge Laplacian acting on differential one-forms. The other is on the connection Laplacian acting on tensor fields of every type, which include all differential forms. These are sharp generalizations of Cheeger-Colding's spectral convergence of the Laplacian acting on functions to the cases of tensor fields and differential forms. These spectral convergence have two direct corollaries. One of them is to give new bounds on such eigenvalues, in terms of bounds on volume, diameter and the Ricci curvature. The other is that we show the upper semicontinuity of the first Betti numbers with respect to the Gromov-Hausdorff topology, and give the equivalence between the continuity of them and the existence of a uniform spectral gap. On the other hand we also define measurable curvature tensors of the noncollapsed Gromov-Hausdorff limit space of a sequence of Riemannian manifolds with a uniform bound of Ricci curvature, which include Riemannian curvature tensor, the Ricci curvature, and the scalar curvature. As fundamental properties of our Ricci curvature, we show that the Ricci curvature coincides with the difference between the Hodge Laplacian and the connection Laplacian, and is compatible with Gigli's one and Lott's Ricci measure. Moreover we prove a lower bound of the Ricci curvature is compatible with a reduced Riemannian curvature dimension condition. We also give a positive answer to Lott's question on the behavior of the scalar curvature with respect to the Gromov-Hausdorff topology by using our scalar curvature. This talk is based on arXiv:1510.05349.

#### FMSP Lectures

15:00-16:00, 16:10-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)

[ Reference URL ]

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

**Aniceto Murillo et al**(Universidad de Malaga)Rational homotopy theory : Quillen and Sullivan approach.(2) (ENGLISH)

[ Reference URL ]

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

### 2016/04/20

#### FMSP Lectures

15:00-16:00, 16:10-17:10 Room #002 (Graduate School of Math. Sci. Bldg.)

Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)

[ Reference URL ]

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

**Aniceto Murillo et al**(Universidad de Malaga)Rational homotopy theory : Quillen and Sullivan approach.(1) (ENGLISH)

[ Reference URL ]

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

#### Number Theory Seminar

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

On periodicity of geodesic continued fractions (Japanese)

**Hoto Bekki**(University of Tokyo)On periodicity of geodesic continued fractions (Japanese)

### 2016/04/19

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Isomorphic quartic K3 surfaces and Cremona transformations (JAPANESE)

**Keiji Oguiso**(University of Tokyo)Isomorphic quartic K3 surfaces and Cremona transformations (JAPANESE)

[ Abstract ]

We show that

(i) there is a pair of smooth complex quartic K3 surfaces such that they are isomorphic as abstract varieties but not Cremona equivalent.

(ii) there is a pair of smooth complex quartic K3 surfaces such that they are Cemona equivalent but not projectively equivalent.

These two results are much inspired by e-mails from Professors Tuyen Truong and J\'anos Koll\'ar.

We show that

(i) there is a pair of smooth complex quartic K3 surfaces such that they are isomorphic as abstract varieties but not Cremona equivalent.

(ii) there is a pair of smooth complex quartic K3 surfaces such that they are Cemona equivalent but not projectively equivalent.

These two results are much inspired by e-mails from Professors Tuyen Truong and J\'anos Koll\'ar.

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Topological rigidity of finite cyclic group actions on compact surfaces (ENGLISH)

**Błażej Szepietowski**(Gdansk University)Topological rigidity of finite cyclic group actions on compact surfaces (ENGLISH)

[ Abstract ]

Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface. I will describe a method of enumeration (and classification) of topological equivalence classes of actions of a finite group on a compact surface, based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short) and a relationship between the outer automorphism group of an NEC group and certain mapping class group. By this method we study topological equivalence of actions of a finite cyclic group on a compact surface, in the situation where the order of the group is large relative to the genus of the surface.

Two actions of a group on a surface are called topologically equivalent if they are conjugate by a homeomorphism of the surface. I will describe a method of enumeration (and classification) of topological equivalence classes of actions of a finite group on a compact surface, based on the combinatorial theory of noneuclidean crystallographic groups (NEC groups in short) and a relationship between the outer automorphism group of an NEC group and certain mapping class group. By this method we study topological equivalence of actions of a finite cyclic group on a compact surface, in the situation where the order of the group is large relative to the genus of the surface.

### 2016/04/18

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

On the functoriality of Haagerup's $L^2$-space construction: Verticalizing decorated 2-categories

**Juan Orendain**(UNAM/Univ. Tokyo)On the functoriality of Haagerup's $L^2$-space construction: Verticalizing decorated 2-categories

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Kunio Obitsu**(Kagoshima University)(JAPANESE)

#### Numerical Analysis Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Error estimate for the finite element method in a smooth domain (日本語)

**Takahito Kashiwabara**(University of Tokyo)Error estimate for the finite element method in a smooth domain (日本語)

#### Tokyo Probability Seminar

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Sharp interface limit for one-dimensional stochastic Allen-Cahn equation with Dirichlet boundary condition

**Kai Lee**(Graduate School of Mathematical Sciences, the university of Tokyo)Sharp interface limit for one-dimensional stochastic Allen-Cahn equation with Dirichlet boundary condition

### 2016/04/14

#### FMSP Lectures

15:30-17:00 Room #Lecture Hall, Kavli IPMU (Graduate School of Math. Sci. Bldg.)

Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)

[ Reference URL ]

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

**Alan Weinstein**(University of California, Berkeley)Lecture 2: Geometric and algebraic Poisson modules (ENGLISH)

[ Reference URL ]

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

### 2016/04/13

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)

(English)

**Akio Tamagawa**(RIMS, Kyoto University)Semisimplicity of geometric monodromy on etale cohomology (joint work with Anna Cadoret and Chun Yin Hui)

(English)

[ Abstract ]

Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient etale cohomology groups of the geometric fiber of X --> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient etale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).

Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient etale cohomology groups of the geometric fiber of X --> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient etale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).

#### FMSP Lectures

13:30-14:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)

[ Reference URL ]

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

**Yavar Kian**(Aix-Marseille Univ.)Determination of time-dependent coefficients for wave equations from partial data (ENGLISH)

[ Reference URL ]

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

### 2016/04/12

#### Lie Groups and Representation Theory

17:00-18:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Universal Gysin formulas for flag bundles

**Piotr Pragacz**(Institute of Mathematics, Polish Academy of Sciences)Universal Gysin formulas for flag bundles

[ Abstract ]

We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.

We give generalizations of the formula for the push-forward of a power of the hyperplane class in a projective bundle to flag bundles of type A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. This is a joint work with Lionel Darondeau.

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