## Seminar information archive

Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～

### 2012/05/14

#### Seminar on Geometric Complex Analysis

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

Duality in the unit circle and the ring of p-adic intergers and van der Corput series (JAPANESE)

**Hiroshi KANEKO**(Tokyo University of Science)Duality in the unit circle and the ring of p-adic intergers and van der Corput series (JAPANESE)

### 2012/05/11

#### Colloquium

16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Moduli spaces and symplectic derivation Lie algebras (JAPANESE)

**SAKASAI Takuya**(University of Tokyo)Moduli spaces and symplectic derivation Lie algebras (JAPANESE)

[ Abstract ]

First we overview Kontsevich's theorem describing a deep connection between homology of certain infinite dimensional Lie algebras (symplectic derivation Lie algebras) and cohomology of various moduli spaces. Then we discuss some computational results on the Lie algebras together with their applications (joint work with Shigeyuki Morita and Masaaki Suzuki).

First we overview Kontsevich's theorem describing a deep connection between homology of certain infinite dimensional Lie algebras (symplectic derivation Lie algebras) and cohomology of various moduli spaces. Then we discuss some computational results on the Lie algebras together with their applications (joint work with Shigeyuki Morita and Masaaki Suzuki).

#### Seminar on Probability and Statistics

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

Efficient Discretization of Stochastic Integrals (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/03.html

**FUKASAWA, Masaaki**(Department of Mathematics, Osaka University)Efficient Discretization of Stochastic Integrals (JAPANESE)

[ Abstract ]

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.

[ Reference URL ]Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly. The result is directly applicable to practical hedging problem in mathematical finance; it gives an asymptotically optimal way to choose rebalancing dates and portofolios with respect to transaction costs. The asymptotically efficient strategies in fact reflect the structure of transaction costs. In particular a specific biased rebalancing scheme is shown to be superior to unbiased schemes if transaction costs follow a convex model. The problem is discussed also in terms of the exponential utility maximization.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/03.html

### 2012/05/08

#### Tuesday Seminar on Topology

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

Infinite examples of non-Garside monoids having fundamental elements (JAPANESE)

**Tadashi Ishibe**(The University of Tokyo, JSPS)Infinite examples of non-Garside monoids having fundamental elements (JAPANESE)

[ Abstract ]

The Garside group, as a generalization of Artin groups,

is defined as the group of fractions of a Garside monoid.

To understand the elliptic Artin groups, which are the fundamental

groups of the complement of discriminant divisors of the semi-versal

deformation of the simply elliptic singularities E_6~, E_7~ and E_8~,

we need to consider another generalization of Artin groups.

In this talk, we will study the presentations of fundamental groups

of the complement of complexified real affine line arrangements

and consider the associated monoids.

It turns out that, in some cases, they are not Garside monoids.

Nevertheless, we will show that they satisfy the cancellation condition

and carry certain particular elements similar to the fundamental elements

in Artin monoids.

As a result, we will show that the word problem can be solved

and the center of them are determined.

The Garside group, as a generalization of Artin groups,

is defined as the group of fractions of a Garside monoid.

To understand the elliptic Artin groups, which are the fundamental

groups of the complement of discriminant divisors of the semi-versal

deformation of the simply elliptic singularities E_6~, E_7~ and E_8~,

we need to consider another generalization of Artin groups.

In this talk, we will study the presentations of fundamental groups

of the complement of complexified real affine line arrangements

and consider the associated monoids.

It turns out that, in some cases, they are not Garside monoids.

Nevertheless, we will show that they satisfy the cancellation condition

and carry certain particular elements similar to the fundamental elements

in Artin monoids.

As a result, we will show that the word problem can be solved

and the center of them are determined.

#### Numerical Analysis Seminar

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

Pressure Oscillation Problem of MPS time evolution scheme for incompressible Navier-Stokes equation (JAPANESE)

[ Reference URL ]

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

**Motofumi Hattori**(Kanagawa Institute of Technology )Pressure Oscillation Problem of MPS time evolution scheme for incompressible Navier-Stokes equation (JAPANESE)

[ Reference URL ]

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

#### Lectures

14:40-16:10 Room #470 (Graduate School of Math. Sci. Bldg.)

Embedding spaces and string topology (JAPANESE)

**Keiichi Sakai**(Shishu University)Embedding spaces and string topology (JAPANESE)

[ Abstract ]

There are several similarities between the topology of embedding spaces and that of (free) loop space.

In this talk I will review the similarities, with a focus on "string topology" for embedding spaces.

There are several similarities between the topology of embedding spaces and that of (free) loop space.

In this talk I will review the similarities, with a focus on "string topology" for embedding spaces.

### 2012/05/07

#### Seminar on Geometric Complex Analysis

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

The second metric variation of the total $Q$-curvature in conformal geometry (JAPANESE)

**Yoshihiko Matsumoto**(University of Tokyo)The second metric variation of the total $Q$-curvature in conformal geometry (JAPANESE)

[ Abstract ]

Branson's $Q$-curvature of even-dimensional compact conformal manifolds integrates to a global conformal invariant called the total $Q$-curvature. While it is topological in two dimensions and is essentially the Weyl action in four dimensions, in the higher dimensional cases its geometric meaning remains mysterious. Graham and Hirachi have shown that the first metric variation of the total $Q$-curvature coincides with the Fefferman-Graham obstruction tensor. In this talk, the second variational formula will be presented, and it will be made explicit especially for conformally Einstein manifolds. The positivity of the second variation will be discussed in connection with the smallest eigenvalue of the Lichnerowicz Laplacian.

Branson's $Q$-curvature of even-dimensional compact conformal manifolds integrates to a global conformal invariant called the total $Q$-curvature. While it is topological in two dimensions and is essentially the Weyl action in four dimensions, in the higher dimensional cases its geometric meaning remains mysterious. Graham and Hirachi have shown that the first metric variation of the total $Q$-curvature coincides with the Fefferman-Graham obstruction tensor. In this talk, the second variational formula will be presented, and it will be made explicit especially for conformally Einstein manifolds. The positivity of the second variation will be discussed in connection with the smallest eigenvalue of the Lichnerowicz Laplacian.

#### Algebraic Geometry Seminar

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

Algebro-geometric characterization of Cayley polytopes (JAPANESE)

**Atsushi Ito**(University of Tokyo)Algebro-geometric characterization of Cayley polytopes (JAPANESE)

[ Abstract ]

A lattice polytope is called a Cayley polytope if it is "small" in some

sense.

In this talk, I will explain an algebro-geometric characterization of

Cayley polytopes

by considering whether or not the corresponding polarized toric

varieties are covered by lines, planes, etc.

We can apply this characterization to the study of Seshadri constants,

which are invariants measuring the positivity of ample line bundles.

That is, we can obtain an explicit description of a polarized toric

variety whose Seshadri constant is one.

A lattice polytope is called a Cayley polytope if it is "small" in some

sense.

In this talk, I will explain an algebro-geometric characterization of

Cayley polytopes

by considering whether or not the corresponding polarized toric

varieties are covered by lines, planes, etc.

We can apply this characterization to the study of Seshadri constants,

which are invariants measuring the positivity of ample line bundles.

That is, we can obtain an explicit description of a polarized toric

variety whose Seshadri constant is one.

#### GCOE Seminars

14:30-16:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Distributional behaviors of time-averaged observables in anomalous diffusions (subdiffusion and superdiffusion) (ENGLISH)

**Takuma Akimoto**(Keio university, Global environmental leaders program)Distributional behaviors of time-averaged observables in anomalous diffusions (subdiffusion and superdiffusion) (ENGLISH)

[ Abstract ]

In anomalous diffusions attributed to a power-law distribution,

time-averaged observables such as diffusion coefficient and velocity of drift are intrinsically random. Anomalous diffusion is ubiquitous phenomenon not only in material science but also in biological transports, which is characterized by a non-linear growth of the mean square displacement (MSD).

(subdiffusion: sublinear growth, super diffusion: superlinear growth).

It has been known that there are three different mechanisms generating subdiffusion. One of them is a power-law distribution in the trapping-time distribution. Such anomalous diffusion is modeled by the continuous time random walk (CTRW). In CTRW, the time-averaged MSD grows linearly with time whereas the ensemble-averaged MSD does not. Using renewal theory, I show that diffusion coefficients obtained by single trajectories converge in distribution. The distribution is the Mittag-Leffler (or inverse Levy) distribution [1,2].

In superdiffusion, there are three different mechanisms. One stems from positive correlations in random walks; the second from persistent motions in random walks, called Levy walk; the third from very long jumps in random walks, called Levy flight.

If the persistent time distribution obeys a power law with divergent mean in Levy walks, the MSD grows as t^2 whereas the mean of positions is zero. When an external bias is added in Levy walks, the response to bias (velocity of drift) appears in the distribution, which is what we term a distributional response [3]. The distribution is the generalized arcsine distribution.

These distributional behaviors open a new window to dealing with the average (ensemble or time average) in single particle tracking experiments.

[1] Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008).

[2] T. Miyaguchi and T. Akimoto, Phys. Rev. E 83, 031926 (2011).

[3] T. Akimoto, Phys. Rev. Lett. 108, 164101 (2012)

In anomalous diffusions attributed to a power-law distribution,

time-averaged observables such as diffusion coefficient and velocity of drift are intrinsically random. Anomalous diffusion is ubiquitous phenomenon not only in material science but also in biological transports, which is characterized by a non-linear growth of the mean square displacement (MSD).

(subdiffusion: sublinear growth, super diffusion: superlinear growth).

It has been known that there are three different mechanisms generating subdiffusion. One of them is a power-law distribution in the trapping-time distribution. Such anomalous diffusion is modeled by the continuous time random walk (CTRW). In CTRW, the time-averaged MSD grows linearly with time whereas the ensemble-averaged MSD does not. Using renewal theory, I show that diffusion coefficients obtained by single trajectories converge in distribution. The distribution is the Mittag-Leffler (or inverse Levy) distribution [1,2].

In superdiffusion, there are three different mechanisms. One stems from positive correlations in random walks; the second from persistent motions in random walks, called Levy walk; the third from very long jumps in random walks, called Levy flight.

If the persistent time distribution obeys a power law with divergent mean in Levy walks, the MSD grows as t^2 whereas the mean of positions is zero. When an external bias is added in Levy walks, the response to bias (velocity of drift) appears in the distribution, which is what we term a distributional response [3]. The distribution is the generalized arcsine distribution.

These distributional behaviors open a new window to dealing with the average (ensemble or time average) in single particle tracking experiments.

[1] Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008).

[2] T. Miyaguchi and T. Akimoto, Phys. Rev. E 83, 031926 (2011).

[3] T. Akimoto, Phys. Rev. Lett. 108, 164101 (2012)

### 2012/05/02

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

A measurable group theoretic solution to von Neumann's Problem (after Gaboriau and Lyons) (JAPANESE)

**Yuhei Suzuki**(Univ. Tokyo)A measurable group theoretic solution to von Neumann's Problem (after Gaboriau and Lyons) (JAPANESE)

### 2012/05/01

#### Tuesday Seminar on Topology

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

Minimal models, formality and hard Lefschetz property of

solvmanifolds with local systems (JAPANESE)

**Hisashi Kasuya**(The University of Tokyo)Minimal models, formality and hard Lefschetz property of

solvmanifolds with local systems (JAPANESE)

### 2012/04/27

#### Seminar on Probability and Statistics

15:00-16:10 Room #006 (Graduate School of Math. Sci. Bldg.)

Convergence conditions on step sizes in temporal difference learning (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/02.html

**NOMURA, Ryosuke**(Graduate school of Mathematical Sciences, Univ. of Tokyo)Convergence conditions on step sizes in temporal difference learning (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/02.html

### 2012/04/25

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Bost-Connes system and class field theory (JAPANESE)

**Takuya Takeishi**(Univ. Tokyo)Bost-Connes system and class field theory (JAPANESE)

### 2012/04/24

#### Numerical Analysis Seminar

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

Quantum mechanics and numerical analysis (JAPANESE)

[ Reference URL ]

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

**Hideaki Ishikawa**(Semiconductor Leading Edge Technologies, Inc.)Quantum mechanics and numerical analysis (JAPANESE)

[ Reference URL ]

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

#### Tuesday Seminar on Topology

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

Combinatorial Heegaard Floer homology (ENGLISH)

**Dylan Thurston**(Columbia University)Combinatorial Heegaard Floer homology (ENGLISH)

[ Abstract ]

Heegaard Floer homology is a powerful invariant of 3- and 4-manifolds.

In 4 dimensions, Heegaard Floer homology (together with the

Seiberg-Witten and Donaldson equations, which are conjecturally

equivalent), provides essentially the only technique for

distinguishing smooth 4-manifolds. In 3 dimensions, it provides much

geometric information, like the simplest representatives of a given

homology class.

In this talk we will focus on recent progress in making Heegaard Floer

homology more computable, including a complete algorithm for computing

it for knots.

Heegaard Floer homology is a powerful invariant of 3- and 4-manifolds.

In 4 dimensions, Heegaard Floer homology (together with the

Seiberg-Witten and Donaldson equations, which are conjecturally

equivalent), provides essentially the only technique for

distinguishing smooth 4-manifolds. In 3 dimensions, it provides much

geometric information, like the simplest representatives of a given

homology class.

In this talk we will focus on recent progress in making Heegaard Floer

homology more computable, including a complete algorithm for computing

it for knots.

### 2012/04/23

#### Algebraic Geometry Seminar

17:10-18:40 Room #122 (Graduate School of Math. Sci. Bldg.)

Motivic integration and wild group actions (JAPANESE)

**Takehiko Yasuda**(Osaka University)Motivic integration and wild group actions (JAPANESE)

[ Abstract ]

The cohomological McKay correspondence proved by Batyrev is the equality of an orbifold invariant

and a stringy invariant. The former is an invariant of a smooth variety with a finite group action and the latter is

an invariant of its quotient variety. Denef and Loeser gave an alternative proof of it which uses the motivic integration theory developped by themselves.

Then I pushed forward with their study by generalizing the motivic integration to

Deligne-Mumford stacks and reformulating the cohomological McKay correspondence from the viewpoint of

the birational geometry of stacks.

However all of these are about tame group actions (the order of a group is not divisible by the characteristic of the base field),

and the wild (= not tame) case has remained unexplored.

In this talk, I will explain my attempt to examine the simplest situation of the wild case. Namely linear actions of a cyclic group

of order equal to the characteristic of the base field are treated. A remarkable new phenomenon is that the space of generalized

arcs is a fibration over an infinite dimensional space with infinite dimensional fibers, where the base space is the space of

Artin-Schreier extensions of $k((t))$, the field of Laurent series.

The cohomological McKay correspondence proved by Batyrev is the equality of an orbifold invariant

and a stringy invariant. The former is an invariant of a smooth variety with a finite group action and the latter is

an invariant of its quotient variety. Denef and Loeser gave an alternative proof of it which uses the motivic integration theory developped by themselves.

Then I pushed forward with their study by generalizing the motivic integration to

Deligne-Mumford stacks and reformulating the cohomological McKay correspondence from the viewpoint of

the birational geometry of stacks.

However all of these are about tame group actions (the order of a group is not divisible by the characteristic of the base field),

and the wild (= not tame) case has remained unexplored.

In this talk, I will explain my attempt to examine the simplest situation of the wild case. Namely linear actions of a cyclic group

of order equal to the characteristic of the base field are treated. A remarkable new phenomenon is that the space of generalized

arcs is a fibration over an infinite dimensional space with infinite dimensional fibers, where the base space is the space of

Artin-Schreier extensions of $k((t))$, the field of Laurent series.

### 2012/04/21

#### Harmonic Analysis Komaba Seminar

13:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Dyadic, classical and martingale harmonic analysis (JAPANESE)

A_\\\\infty constants between BMO and weighted BMO (JAPANESE)

**Yutaka, Terasawa**(Graduate School of Mathematical Sciences, University of Tokyo) 13:30-15:00Dyadic, classical and martingale harmonic analysis (JAPANESE)

[ Abstract ]

**Yohei Tsutsui**(Waseda University) 15:30-17:00A_\\\\infty constants between BMO and weighted BMO (JAPANESE)

[ Abstract ]

### 2012/04/20

#### Seminar on Probability and Statistics

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

On the asymptotic mixed normality of the pre-averaged Hayashi-Yoshida

estimator with random and nonsynchronous sampling (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/01.html

**KOIKE, Yuta**(Graduate school of Mathematical Sciences, Univ. of Tokyo)On the asymptotic mixed normality of the pre-averaged Hayashi-Yoshida

estimator with random and nonsynchronous sampling (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/01.html

### 2012/04/18

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

Explicit constructions of rational points on elliptic curves (ENGLISH)

**Alan Lauder**(University of Oxford)Explicit constructions of rational points on elliptic curves (ENGLISH)

[ Abstract ]

I will present an algorithm for computing certain special

values of p-adic L-functions, and discuss an application to

the efficient construction of rational points on elliptic curves.

I will present an algorithm for computing certain special

values of p-adic L-functions, and discuss an application to

the efficient construction of rational points on elliptic curves.

#### Operator Algebra Seminars

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Classification of Group Actions on Factors (after Masuda) (JAPANESE)

**Koichi Shimada**(Univ. Tokyo)Classification of Group Actions on Factors (after Masuda) (JAPANESE)

### 2012/04/17

#### Tuesday Seminar on Topology

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

Pseudo-Anosov mapping classes with small dilatation (ENGLISH)

**Eriko Hironaka**(Florida State University)Pseudo-Anosov mapping classes with small dilatation (ENGLISH)

[ Abstract ]

A mapping class is a homeomorphism of an oriented surface

to itself modulo isotopy. It is pseudo-Anosov if the lengths of essential

simple closed curves under iterations of the map have exponential growth

rate. The growth rate, an algebraic integer of degree bounded with

respect to the topology of the surface, is called the dilatation of the

mapping class. In this talk we will discuss the minimization problem

for dilatations of pseudo-Anosov mapping classes, and give two general

constructions of pseudo-Anosov mapping classes with small dilatation.

A mapping class is a homeomorphism of an oriented surface

to itself modulo isotopy. It is pseudo-Anosov if the lengths of essential

simple closed curves under iterations of the map have exponential growth

rate. The growth rate, an algebraic integer of degree bounded with

respect to the topology of the surface, is called the dilatation of the

mapping class. In this talk we will discuss the minimization problem

for dilatations of pseudo-Anosov mapping classes, and give two general

constructions of pseudo-Anosov mapping classes with small dilatation.

### 2012/04/16

#### Algebraic Geometry Seminar

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

Toric degenerations of minuscule Schubert varieties and mirror symmetry (JAPANESE)

**Makoto Miura**(University of Tokyo)Toric degenerations of minuscule Schubert varieties and mirror symmetry (JAPANESE)

[ Abstract ]

Minuscule Schubert varieties admit the flat degenerations to projective

Hibi toric varieties, whose combinatorial structure is explicitly

described by finite posets. In this talk, I will explain these toric

degenerations and discuss the mirror symmetry for complete intersection

Calabi-Yau varieties in Gorenstein minuscule Schubert varieties.

Minuscule Schubert varieties admit the flat degenerations to projective

Hibi toric varieties, whose combinatorial structure is explicitly

described by finite posets. In this talk, I will explain these toric

degenerations and discuss the mirror symmetry for complete intersection

Calabi-Yau varieties in Gorenstein minuscule Schubert varieties.

#### Seminar on Geometric Complex Analysis

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

Fekete configuration, quantitative equidistribution and wanderting critical orbits in non-archimedean dynamics

(JAPANESE)

**Yusuke Okuyama**(Kyoto Institute of Technology)Fekete configuration, quantitative equidistribution and wanderting critical orbits in non-archimedean dynamics

(JAPANESE)

### 2012/04/14

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)

Moments of the derivatives of the Riemann zeta function (JAPANESE)

**Kazutoshi Kariyama**(Onomichi city university) 13:30-14:30Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)

**Keijyu Souno**(Math.-Sci., Tokyo Univ.) 15:00-16:00Moments of the derivatives of the Riemann zeta function (JAPANESE)

[ Abstract ]

In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

### 2012/04/13

#### Seminar on Probability and Statistics

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

Asymptotic properties of MCMC for cumulative link model (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/00.html

**KAMATANI, Kengo**(Graduate School of Engineering Science, Osaka University)Asymptotic properties of MCMC for cumulative link model (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2012/00.html

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183 Next >