## Seminar information archive

Seminar information archive ～02/01｜Today's seminar 02/02 | Future seminars 02/03～

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Value distribution of meromorphic functions on foliated manifolds,II (JAPANESE)

**Atsushi Atsuji**(Keio University)Value distribution of meromorphic functions on foliated manifolds,II (JAPANESE)

### 2012/10/26

#### Seminar on Probability and Statistics

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

Tuning parameter selection in sparse regression modeling (JAPANESE)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html

**HIROSE, Kei**(Graduate School of Engineering Science, Osaka University)Tuning parameter selection in sparse regression modeling (JAPANESE)

[ Abstract ]

In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.

[ Reference URL ]In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' Cp type criteria may be used as a tuning parameter selection tool in lasso type regularization methods, for which the concept of degrees of freedom plays a key role. In this talk, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and nonconvex penalties. The proposed methodology is investigated through the analysis of real data and Monte Carlo simulations. Numerical results show that Cp criterion based on our algorithm performs well in various situations.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/10.html

### 2012/10/23

#### Tuesday Seminar of Analysis

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Topics in quantum entropy and entanglement (ENGLISH)

**Elliott Lieb**(Princeton Univ.)Topics in quantum entropy and entanglement (ENGLISH)

[ Abstract ]

Several recent results on quantum entropy and the uncertainty

principle will be discussed. This is partly joint work with Eric Carlen

on lower bounds for entanglement, which has no classical analog, in terms

of the negative of the conditional entropy, S1 - S12, whose negativity,

when it occurs, also has no classical analog. (see arXiv:1203.4719)

It is also partly joint work with Rupert Frank on the uncertaintly

principle for quantum entropy which compares the quantum von Neumann

entropy with the classical entropies with respect to two different

bases. We prove an extension to the product of two and three spaces, which

has applications in quantum information theory. (see arxiv:1204.0825)

Several recent results on quantum entropy and the uncertainty

principle will be discussed. This is partly joint work with Eric Carlen

on lower bounds for entanglement, which has no classical analog, in terms

of the negative of the conditional entropy, S1 - S12, whose negativity,

when it occurs, also has no classical analog. (see arXiv:1203.4719)

It is also partly joint work with Rupert Frank on the uncertaintly

principle for quantum entropy which compares the quantum von Neumann

entropy with the classical entropies with respect to two different

bases. We prove an extension to the product of two and three spaces, which

has applications in quantum information theory. (see arxiv:1204.0825)

#### Tuesday Seminar on Topology

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

A geometric approach to the Johnson homomorphisms (JAPANESE)

**Nariya Kawazumi**(The University of Tokyo)A geometric approach to the Johnson homomorphisms (JAPANESE)

[ Abstract ]

We re-construct the Johnson homomorphisms as an embeddig of the Torelli

group

into the completed Goldman-Turaev Lie bialgebra. Then the image is

included in the

kernel of the Turaev cobracket. In the case where the boundary is

connected,

the Turaev cobracket clarifies a geometric meaning of the Morita traces.

Time permitting, we also discuss the case of holed discs.

This talk is based on a joint work with Yusuke Kuno (Tsuda College).

We re-construct the Johnson homomorphisms as an embeddig of the Torelli

group

into the completed Goldman-Turaev Lie bialgebra. Then the image is

included in the

kernel of the Turaev cobracket. In the case where the boundary is

connected,

the Turaev cobracket clarifies a geometric meaning of the Morita traces.

Time permitting, we also discuss the case of holed discs.

This talk is based on a joint work with Yusuke Kuno (Tsuda College).

### 2012/10/22

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

The second main therorem for entire curves into Hilbert modular surfaces (JAPANESE)

**Yusaku Tiba**(Grad. School of Math. Sci., Univ. of Tokyo)The second main therorem for entire curves into Hilbert modular surfaces (JAPANESE)

### 2012/10/19

#### Seminar on Probability and Statistics

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

Asymptotic expansion of ruin probability under Lévy insurance risks (JAPANESE)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/09.html

**SHIMIZU, Yasutaka**(Graduate School of Engineering Science, Osaka University)Asymptotic expansion of ruin probability under Lévy insurance risks (JAPANESE)

[ Abstract ]

An asymptotic expansion formula of the ultimate ruin probability under L\\'evy insurance risks

is given as the loading factor tends to zero. The formula is obtained via the Edgeworth type expansion of

the compound geometric random sum. We give higher-order expansions of the ruin probability with a certain validity.

This allows us to evaluate quantile of the ruin function, which is nicely applied to estimate the VaR-type risk measure due to ruin.

[ Reference URL ]An asymptotic expansion formula of the ultimate ruin probability under L\\'evy insurance risks

is given as the loading factor tends to zero. The formula is obtained via the Edgeworth type expansion of

the compound geometric random sum. We give higher-order expansions of the ruin probability with a certain validity.

This allows us to evaluate quantile of the ruin function, which is nicely applied to estimate the VaR-type risk measure due to ruin.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/09.html

### 2012/10/18

#### Seminar on Probability and Statistics

15:15-16:25 Room #006 (Graduate School of Math. Sci. Bldg.)

Quasi-Bayesian analysis of nonparametric instrumental variables models (JAPANESE)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/08.html

**KATO, Kengo**(Department of Mathematics, Graduate School of Science, Hiroshima University)Quasi-Bayesian analysis of nonparametric instrumental variables models (JAPANESE)

[ Abstract ]

This paper aims at developing a quasi-Bayesian analysis

of the nonparametric instrumental variables model, with a focus on the

asymptotic properties of quasi-posterior distributions. In this paper,

instead of assuming a distributional assumption on the data generating

process, we consider a quasi-likelihood induced from the conditional

moment restriction, and put priors on the function-valued parameter.

We call the resulting posterior quasi-posterior, which corresponds to

``Gibbs posterior'' in the literature. Here we shall focus on sieve

priors, which are priors that concentrate on finite dimensional sieve

spaces. The dimension of the sieve space should increase as the sample

size. We derive rates of contraction and a non-parametric Bernstein-von

Mises type result for the quasi-posterior distribution, and rates of

convergence for the quasi-Bayes estimator defined by the posterior

expectation. We show that, with priors suitably chosen, the

quasi-posterior distribution (the quasi-Bayes estimator) attains the

minimax optimal rate of contraction (convergence, respectively). These

results greatly sharpen the previous related work.

[ Reference URL ]This paper aims at developing a quasi-Bayesian analysis

of the nonparametric instrumental variables model, with a focus on the

asymptotic properties of quasi-posterior distributions. In this paper,

instead of assuming a distributional assumption on the data generating

process, we consider a quasi-likelihood induced from the conditional

moment restriction, and put priors on the function-valued parameter.

We call the resulting posterior quasi-posterior, which corresponds to

``Gibbs posterior'' in the literature. Here we shall focus on sieve

priors, which are priors that concentrate on finite dimensional sieve

spaces. The dimension of the sieve space should increase as the sample

size. We derive rates of contraction and a non-parametric Bernstein-von

Mises type result for the quasi-posterior distribution, and rates of

convergence for the quasi-Bayes estimator defined by the posterior

expectation. We show that, with priors suitably chosen, the

quasi-posterior distribution (the quasi-Bayes estimator) attains the

minimax optimal rate of contraction (convergence, respectively). These

results greatly sharpen the previous related work.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/08.html

#### Lectures

16:00-17:00 Room #470 (Graduate School of Math. Sci. Bldg.)

Multidimensional ill-posed problems (ENGLISH)

**Anatoly Yagola**(Lomonosov Moscow State University)Multidimensional ill-posed problems (ENGLISH)

[ Abstract ]

It is very important now to develop methods of solving multidimensional ill-posed problems using regularization procedures and parallel computers. The main purpose of the talk is to show how 2D and 3D Fredholm integral equations of the 1st kind can be effectively solved.

We will consider ill-posed problems on compact sets of convex functions [1] and functions convex along lines parallel to coordinate axes [2].

Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the permanent magnetization due to the complications of magnetization distributions over the ship body, and errors and noises of measurement data degrade the accuracy and quality of the parameter identification. In this paper, we use a two step sequential solutions to solve the inversion problem. In the first step, a numerical model is built and used to determine the induced magnetization of the ship. In the second step, we solve a type of continuous magnetization inversion problem by solving 2D and 3D Fredholm integral

equations of the 1st kind. We use parallel computing which allows solve the inverse problem with high accuracy. Tikhonov regularization has been applied in solving the inversion problems. The proposed methods have been validated using simulation data with added noises [4, 6].

2D and 3D inverse problems also could be found in tomography [3] and electron microscopy [5]. We will demonstrate examples of applied problems and discuss methods of numerical solving.

This paper was supported by the Visby program and RFBR grants 11-01-00040–а and 12-01-91153-NSFC-a.

It is very important now to develop methods of solving multidimensional ill-posed problems using regularization procedures and parallel computers. The main purpose of the talk is to show how 2D and 3D Fredholm integral equations of the 1st kind can be effectively solved.

We will consider ill-posed problems on compact sets of convex functions [1] and functions convex along lines parallel to coordinate axes [2].

Recovery of magnetic target parameters from magnetic sensor measurements has attracted wide interests and found many practical applications. However, difficulties present in identifying the permanent magnetization due to the complications of magnetization distributions over the ship body, and errors and noises of measurement data degrade the accuracy and quality of the parameter identification. In this paper, we use a two step sequential solutions to solve the inversion problem. In the first step, a numerical model is built and used to determine the induced magnetization of the ship. In the second step, we solve a type of continuous magnetization inversion problem by solving 2D and 3D Fredholm integral

equations of the 1st kind. We use parallel computing which allows solve the inverse problem with high accuracy. Tikhonov regularization has been applied in solving the inversion problems. The proposed methods have been validated using simulation data with added noises [4, 6].

2D and 3D inverse problems also could be found in tomography [3] and electron microscopy [5]. We will demonstrate examples of applied problems and discuss methods of numerical solving.

This paper was supported by the Visby program and RFBR grants 11-01-00040–а and 12-01-91153-NSFC-a.

### 2012/10/17

#### Geometry Colloquium

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

p-Kazhdan constants and non-expanders (JAPANESE)

**Masato Mimura**(Tohoku University)p-Kazhdan constants and non-expanders (JAPANESE)

[ Abstract ]

In study of graphs and finitely generated groups (as Cayley graphs) as metric spaces with the path metrics, one basic idea is to "linearize" them, more precisely, to embed them into certain Banach spaces in some nice way. Special attention has been paid to embeddings of graphs into Hilbert spaces or l^p spaces. It is a well-known result that a "family of expanders", namely, a family of finite graphs (of unifromly bounded degree) with uniform lower bound of spectral gaps (equivalently, of Cheeger constants), does not coarsely embed into Hilbert spaces, or l^p spaces.

In this talk, we investigate a "family of NON-expanders" coming from Cayley graphs of a family of finitely generated groups. In this setting we define l^p-version of the Kazhdan constant and of the property tau constant for groups, and study the decay rate of p-spectral gap of non-expanders in terms of them. This gives some metric geometrical information on the family. Our main example will be the family of (Cayley graphs of SL_n(Z/k_nZ)), indexed by n>2, for (k_n)_n a sequence of natural numbers>2 and with respect to standard 4-element generating sets. We will start from basic definitions, such as ones of Cayley graphs, expander families, and Kazhdan constants.

In study of graphs and finitely generated groups (as Cayley graphs) as metric spaces with the path metrics, one basic idea is to "linearize" them, more precisely, to embed them into certain Banach spaces in some nice way. Special attention has been paid to embeddings of graphs into Hilbert spaces or l^p spaces. It is a well-known result that a "family of expanders", namely, a family of finite graphs (of unifromly bounded degree) with uniform lower bound of spectral gaps (equivalently, of Cheeger constants), does not coarsely embed into Hilbert spaces, or l^p spaces.

In this talk, we investigate a "family of NON-expanders" coming from Cayley graphs of a family of finitely generated groups. In this setting we define l^p-version of the Kazhdan constant and of the property tau constant for groups, and study the decay rate of p-spectral gap of non-expanders in terms of them. This gives some metric geometrical information on the family. Our main example will be the family of (Cayley graphs of SL_n(Z/k_nZ)), indexed by n>2, for (k_n)_n a sequence of natural numbers>2 and with respect to standard 4-element generating sets. We will start from basic definitions, such as ones of Cayley graphs, expander families, and Kazhdan constants.

#### Lectures

15:00-16:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Inverse problems for differential operators on spatial networks (ENGLISH)

**Vjacheslav Yurko**(Saratov University)Inverse problems for differential operators on spatial networks (ENGLISH)

### 2012/10/16

#### Tuesday Seminar on Topology

17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)

Analytic torsion of log-Enriques surfaces (JAPANESE)

**Ken-Ichi Yoshikawa**(Kyoto University)Analytic torsion of log-Enriques surfaces (JAPANESE)

[ Abstract ]

Log-Enriques surfaces are rational surfaces with nowhere vanishing

pluri-canonical forms. We report the recent progress on the computation

of analytic torsion of log-Enriques surfaces.

Log-Enriques surfaces are rational surfaces with nowhere vanishing

pluri-canonical forms. We report the recent progress on the computation

of analytic torsion of log-Enriques surfaces.

### 2012/10/15

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

An L^2 estimate on domains and application to Levi-flat surfaces (JAPANESE)

**Takeo Ohsawa**(Nagoya University)An L^2 estimate on domains and application to Levi-flat surfaces (JAPANESE)

#### Algebraic Geometry Seminar

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

On the moduli b-divisors of lc-trivial fibrations (JAPANESE)

**Yoshinori Gongyo**(University of Tokyo)On the moduli b-divisors of lc-trivial fibrations (JAPANESE)

[ Abstract ]

Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro's result on klt-trivial fibrations. Moreover I may explain some applications of canonical bundle formulas. These are joint works with Osamu Fujino.

Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro's result on klt-trivial fibrations. Moreover I may explain some applications of canonical bundle formulas. These are joint works with Osamu Fujino.

### 2012/10/12

#### Colloquium

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Homogenization on arbitrary manifolds (ENGLISH)

**Antonio Siconolfi**(La Sapienza - University of Rome)Homogenization on arbitrary manifolds (ENGLISH)

[ Abstract ]

We show that results on periodic homogenization for Hamilton-Jacobi equations can be generalized replacing the torus by an arbitrary compact manifold. This allows to reach a deeper understanding of the matter and unveils phenomena somehow hidden in the periodic case, for instance the fact that the ambient spaces of oscillating equations and that of the limit problem are different, and possess even different dimensions. Repetition structure for the base manifold, changes of scale in it and asymptotic analysis, which are the basic ingredients of homogenization, need substantial modification to work in the new frame, and this task is partially accomplished using tools from algebraic topology. An adapted notion of convergence allowing approximating entities and limit to lie in different spaces is also provided.

We show that results on periodic homogenization for Hamilton-Jacobi equations can be generalized replacing the torus by an arbitrary compact manifold. This allows to reach a deeper understanding of the matter and unveils phenomena somehow hidden in the periodic case, for instance the fact that the ambient spaces of oscillating equations and that of the limit problem are different, and possess even different dimensions. Repetition structure for the base manifold, changes of scale in it and asymptotic analysis, which are the basic ingredients of homogenization, need substantial modification to work in the new frame, and this task is partially accomplished using tools from algebraic topology. An adapted notion of convergence allowing approximating entities and limit to lie in different spaces is also provided.

### 2012/10/09

#### Tuesday Seminar on Topology

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

The growth series of pure Artin groups of dihedral type (JAPANESE)

**Michihiko Fujii**(Kyoto University)The growth series of pure Artin groups of dihedral type (JAPANESE)

[ Abstract ]

In this talk, I consider the kernel of the natural projection from

the Artin group of dihedral type to the corresponding Coxeter group,

that we call a pure Artin group of dihedral type,

and present rational function expressions for both the spherical and

geodesic growth series

of the pure Artin group of dihedral type with respect to a natural

generating set.

Also, I show that their growth rates are Pisot numbers.

This talk is partially based on a joint work with Takao Satoh.

In this talk, I consider the kernel of the natural projection from

the Artin group of dihedral type to the corresponding Coxeter group,

that we call a pure Artin group of dihedral type,

and present rational function expressions for both the spherical and

geodesic growth series

of the pure Artin group of dihedral type with respect to a natural

generating set.

Also, I show that their growth rates are Pisot numbers.

This talk is partially based on a joint work with Takao Satoh.

#### Numerical Analysis Seminar

16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

On the numerical verification method for parabolic problems (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

**Takuma Kimura**(Waseda University)On the numerical verification method for parabolic problems (JAPANESE)

[ Reference URL ]

http://www.infsup.jp/utnas/

### 2012/10/06

#### Harmonic Analysis Komaba Seminar

13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Method of rotations with weight for nonisotropic dilations (JAPANESE)

TBA (JAPANESE)

**Shuichi Sato**(Kanazawa university) 13:30-15:00Method of rotations with weight for nonisotropic dilations (JAPANESE)

**( ) 15:30-17:00**TBA (JAPANESE)

### 2012/10/05

#### Seminar on Probability and Statistics

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

Quasi-likelihood analysis for stochastic regression models from nonsynchronous observations (JAPANESE)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/07.html

**OGIHARA, Teppei**(Center for the Study of Finance and Insurance, Osaka University)Quasi-likelihood analysis for stochastic regression models from nonsynchronous observations (JAPANESE)

[ Abstract ]

高頻度金融時系列データの解析時に, 二資産価格データの共変動を解析する上での問題として

"観測の非同期性"がある. データの線形補完や直前データを用いた補完などによるシンプルな

"同期化"を行ったデータに対する共分散推定量は深刻なバイアスが存在することが知られている.

Hayashi and Yoshida (2005)では, 非同期観測下での共分散のノンパラメトリックな不偏推定量を提案し,

推定量の一致性, 漸近(混合)正規性などを示している.

本発表ではパラメータ付2次元拡散過程の非同期観測の問題に対する, 尤度解析を用いたアプローチを紹介し,

最尤型推定量, ベイズ型推定量の構築とその一致性, 漸近混合正規性に関する結果を紹介する.

[ Reference URL ]高頻度金融時系列データの解析時に, 二資産価格データの共変動を解析する上での問題として

"観測の非同期性"がある. データの線形補完や直前データを用いた補完などによるシンプルな

"同期化"を行ったデータに対する共分散推定量は深刻なバイアスが存在することが知られている.

Hayashi and Yoshida (2005)では, 非同期観測下での共分散のノンパラメトリックな不偏推定量を提案し,

推定量の一致性, 漸近(混合)正規性などを示している.

本発表ではパラメータ付2次元拡散過程の非同期観測の問題に対する, 尤度解析を用いたアプローチを紹介し,

最尤型推定量, ベイズ型推定量の構築とその一致性, 漸近混合正規性に関する結果を紹介する.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/07.html

### 2012/10/02

#### Tuesday Seminar on Topology

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

Geometric flows and their self-similar solutions

(JAPANESE)

**Akito Futaki**(The University of Tokyo)Geometric flows and their self-similar solutions

(JAPANESE)

[ Abstract ]

In the first half of this expository talk we consider the Ricci flow and its self-similar solutions,

namely the Ricci solitons. We then specialize in the K\\"ahler case and discuss on the K\\"ahler-Einstein

problem. In the second half of this talk we consider the mean curvature flow and its self-similar

solutions, and see common aspects of the two geometric flows.

In the first half of this expository talk we consider the Ricci flow and its self-similar solutions,

namely the Ricci solitons. We then specialize in the K\\"ahler case and discuss on the K\\"ahler-Einstein

problem. In the second half of this talk we consider the mean curvature flow and its self-similar

solutions, and see common aspects of the two geometric flows.

### 2012/10/01

#### Algebraic Geometry Seminar

13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Weak Lefschetz for divisors (ENGLISH)

**Robert Laterveer**(CNRS, IRMA, Université de Strasbourg)Weak Lefschetz for divisors (ENGLISH)

[ Abstract ]

Let $X$ be a complex projective variety (possibly singular), and $Y\\subset X$ a generic hyperplane section. We prove several weak Lefschetz results concerning the restriction $A^1(X)_{\\qq}\\to A^1(Y)_{\\qq}$, where $A^1$ denotes Fulton--MacPherson's operational Chow cohomology group. In addition, we reprove (and slightly extend) a weak Lefschetz result concerning the Chow group of Weil divisors first proven by Ravindra and Srinivas. As an application of these weak Lefschetz results, we can say something about when the natural map from the Picard group to $A^1$ is an isomorphism.

Let $X$ be a complex projective variety (possibly singular), and $Y\\subset X$ a generic hyperplane section. We prove several weak Lefschetz results concerning the restriction $A^1(X)_{\\qq}\\to A^1(Y)_{\\qq}$, where $A^1$ denotes Fulton--MacPherson's operational Chow cohomology group. In addition, we reprove (and slightly extend) a weak Lefschetz result concerning the Chow group of Weil divisors first proven by Ravindra and Srinivas. As an application of these weak Lefschetz results, we can say something about when the natural map from the Picard group to $A^1$ is an isomorphism.

#### Algebraic Geometry Seminar

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

Frobenius morphisms and derived categories on two dimensional toric Deligne--Mumford stacks (JAPANESE)

**Ryo Ohkawa**(RIMS, Kyoto University)Frobenius morphisms and derived categories on two dimensional toric Deligne--Mumford stacks (JAPANESE)

[ Abstract ]

For a toric Deligne-Mumford (DM) stack over the complex number field, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism of a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the bounded derived category of coherent sheaves on the stack. This is joint work with Hokuto Uehara.

For a toric Deligne-Mumford (DM) stack over the complex number field, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism of a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the bounded derived category of coherent sheaves on the stack. This is joint work with Hokuto Uehara.

### 2012/09/20

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Fusco-Rocha meanders: from Temperley-Lieb algebras to black holes

(ENGLISH)

**Bernold Fiedler**(Free University of Berlin)Fusco-Rocha meanders: from Temperley-Lieb algebras to black holes

(ENGLISH)

[ Abstract ]

Fusco and Rocha studied Neumann boundary value problems for ODEs of second order via a shooting approach. They introduced the notion of what we now call Sturm permutation. These permutation relate, on the one hand, to a special class of meandering curves as introduced by Arnol'd in a singularity context. On the other hand, their special class became central in the study of global attractors of parabolic PDEs of Sturm type.

We discuss relations of Fusco-Rocha meanders with further areas: the multiplicative and trace structure in Temperley-Lieb algebras, discrete versions of Cartesian billiards, and the problem of constructing initial conditions for black hole dynamics which satisfy the Einstein constraints. We also risk a brief glimpse at the long and meandric history of meander patterns themselves.

This is joint work with Juliette Hell, Brian Smith, Carlos Rocha, Pablo Castaneda, and Matthias Wolfrum.

Fusco and Rocha studied Neumann boundary value problems for ODEs of second order via a shooting approach. They introduced the notion of what we now call Sturm permutation. These permutation relate, on the one hand, to a special class of meandering curves as introduced by Arnol'd in a singularity context. On the other hand, their special class became central in the study of global attractors of parabolic PDEs of Sturm type.

We discuss relations of Fusco-Rocha meanders with further areas: the multiplicative and trace structure in Temperley-Lieb algebras, discrete versions of Cartesian billiards, and the problem of constructing initial conditions for black hole dynamics which satisfy the Einstein constraints. We also risk a brief glimpse at the long and meandric history of meander patterns themselves.

This is joint work with Juliette Hell, Brian Smith, Carlos Rocha, Pablo Castaneda, and Matthias Wolfrum.

### 2012/09/15

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Matrix coefficients of the large discrete series of SU(2,1) and SU(3,1) (JAPANESE)

Strict positivity of the central values of some Rankin L-functions of GSp(1,1) and special values of hypergeometric functions (JAPANESE)

**Tadashi Miyazaki**(Kitazato University) 13:30-14:30Matrix coefficients of the large discrete series of SU(2,1) and SU(3,1) (JAPANESE)

**Hiro-aki Narita**(Kumamoto University) 15:00-16:00Strict positivity of the central values of some Rankin L-functions of GSp(1,1) and special values of hypergeometric functions (JAPANESE)

[ Abstract ]

We discuss the strict positivity of the central values of certain convolution type L-functions for several theta lifts to GSp(1,1). Such strict positivity is closely related to special values of some hypergeometric functions.

We discuss the strict positivity of the central values of certain convolution type L-functions for several theta lifts to GSp(1,1). Such strict positivity is closely related to special values of some hypergeometric functions.

### 2012/09/04

#### Tuesday Seminar on Topology

17:00-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Poincare inequalities, rigid groups and applications (ENGLISH)

**Piotr Nowak**(the Institute of Mathematics, Polish Academy of Sciences)Poincare inequalities, rigid groups and applications (ENGLISH)

[ Abstract ]

Kazhdan’s property (T) for a group G can be expressed as a

fixed point property for affine isometric actions of G on a Hilbert

space. This definition generalizes naturally to other normed spaces. In

this talk we will focus on the spectral (aka geometric) method for

proving property (T), based on the work of Garland and studied earlier

by Pansu, Zuk, Ballmann-Swiatkowski, Dymara-Januszkiewicz

(“lambda_1>1/2” conditions) and we generalize it to to the setting of

all reflexive Banach spaces.

As applications we will show estimates of the conformal dimension of the

boundary of random hyperbolic groups in the Gromov density model and

present progress on Shalom’s conjecture on vanishing of 1-cohomology

with coefficients in uniformly bounded representations on Hilbert spaces.

Kazhdan’s property (T) for a group G can be expressed as a

fixed point property for affine isometric actions of G on a Hilbert

space. This definition generalizes naturally to other normed spaces. In

this talk we will focus on the spectral (aka geometric) method for

proving property (T), based on the work of Garland and studied earlier

by Pansu, Zuk, Ballmann-Swiatkowski, Dymara-Januszkiewicz

(“lambda_1>1/2” conditions) and we generalize it to to the setting of

all reflexive Banach spaces.

As applications we will show estimates of the conformal dimension of the

boundary of random hyperbolic groups in the Gromov density model and

present progress on Shalom’s conjecture on vanishing of 1-cohomology

with coefficients in uniformly bounded representations on Hilbert spaces.

### 2012/08/29

#### thesis presentations

10:30-11:45 Room #123 (Graduate School of Math. Sci. Bldg.)

Studies on the asymptotic invariants of cohomology groups and the positivity in complex geometry (JAPANESE)

**Shinichi MATSUMURA**(Graduate School of Mathematical Sciences the University of Tokyo)Studies on the asymptotic invariants of cohomology groups and the positivity in complex geometry (JAPANESE)

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