## Seminar information archive

Seminar information archive ～08/18｜Today's seminar 08/19 | Future seminars 08/20～

#### Numerical Analysis Seminar

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

Hybridized discontinuous Galerkin method for a convection-diffusion equation (JAPANESE)

[ Reference URL ]

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

**Issei Oikawa**(University of Tokyo)Hybridized discontinuous Galerkin method for a convection-diffusion equation (JAPANESE)

[ Reference URL ]

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

### 2010/07/27

#### Tuesday Seminar on Topology

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

Quandle homology and complex volume

(Joint work with Yuichi Kabaya) (JAPANESE)

**Ayumu Inoue**(Tokyo Institute of Technology)Quandle homology and complex volume

(Joint work with Yuichi Kabaya) (JAPANESE)

[ Abstract ]

For a hyperbolic 3-manifold M, the complex value (Vol(M) + i CS(M)) is called the complex volume of M. Here, Vol(M) denotes the volume of M, and CS(M) the Chern-Simons invariant of M.

In 2004, Neumann defined the extended Bloch group, and showed that there is an element of the extended Bloch group corresponding to a hyperbolic 3-manifold.

He further showed that we can compute the complex volume of the manifold by evaluating the element of the extended Bloch group.

To obtain an element of the extended Bloch group corresponding to a hyperbolic 3-manifold, we have to find an ideal triangulation of the manifold and to solve several equations.

On the other hand, we show that the element of the extended Bloch group corresponding to the exterior of a hyperbolic link is obtained from a quandle shadow coloring.

It means that we can compute the complex volume combinatorially from a link diagram.

For a hyperbolic 3-manifold M, the complex value (Vol(M) + i CS(M)) is called the complex volume of M. Here, Vol(M) denotes the volume of M, and CS(M) the Chern-Simons invariant of M.

In 2004, Neumann defined the extended Bloch group, and showed that there is an element of the extended Bloch group corresponding to a hyperbolic 3-manifold.

He further showed that we can compute the complex volume of the manifold by evaluating the element of the extended Bloch group.

To obtain an element of the extended Bloch group corresponding to a hyperbolic 3-manifold, we have to find an ideal triangulation of the manifold and to solve several equations.

On the other hand, we show that the element of the extended Bloch group corresponding to the exterior of a hyperbolic link is obtained from a quandle shadow coloring.

It means that we can compute the complex volume combinatorially from a link diagram.

#### thesis presentations

16:00-17:15 Room #123 (Graduate School of Math. Sci. Bldg.)

On some algebraic properties of CM-types of CM-fields and their reflexes (JAPANESE)

**Ryoko TOMIYASU**(graduate school of Mathematical Sciences)On some algebraic properties of CM-types of CM-fields and their reflexes (JAPANESE)

### 2010/07/22

#### Operator Algebra Seminars

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

$W^*$ Rigidity for actions of wreath product groups (ENGLISH)

**Owen Sizemore**(UCLA)$W^*$ Rigidity for actions of wreath product groups (ENGLISH)

[ Abstract ]

The past 8 years have seen much progress in the classification of

actions of groups on measure spaces. Much of this is due to new powerful

techniques in operator algebras. We will survey some of these results

as well as the new operator algebra techniques. We will then give new

results concerning the classification of actions of wreath product groups.

The past 8 years have seen much progress in the classification of

actions of groups on measure spaces. Much of this is due to new powerful

techniques in operator algebras. We will survey some of these results

as well as the new operator algebra techniques. We will then give new

results concerning the classification of actions of wreath product groups.

### 2010/07/20

#### Tuesday Seminar on Topology

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

A polynomial invariant of pseudo-Anosov maps (JAPANESE)

**Keiko Kawamuro**(University of Iowa)A polynomial invariant of pseudo-Anosov maps (JAPANESE)

[ Abstract ]

Thurston-Nielsen classified surface homomorphism into three classes. Among them, the pseudo-Anosov class is the most interesting since there is strong connection to the hyperbolic manifolds. As an invariant, the dilatation number has been known. In this talk, I will introduce a new invariant of pseudo-Anosov maps. It is an integer coefficient polynomial, which contains the dilatation as the largest real root and is often reducible. I will show properties of the polynomials, examples, and some application to knot theory. (This is a joint work with Joan Birman and Peter Brinkmann.)

Thurston-Nielsen classified surface homomorphism into three classes. Among them, the pseudo-Anosov class is the most interesting since there is strong connection to the hyperbolic manifolds. As an invariant, the dilatation number has been known. In this talk, I will introduce a new invariant of pseudo-Anosov maps. It is an integer coefficient polynomial, which contains the dilatation as the largest real root and is often reducible. I will show properties of the polynomials, examples, and some application to knot theory. (This is a joint work with Joan Birman and Peter Brinkmann.)

### 2010/07/15

#### Lie Groups and Representation Theory

14:30-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Pieri rule and Pieri algebras for the orthogonal groups (ENGLISH)

**Soo Teck Lee**(Singapore National University)Pieri rule and Pieri algebras for the orthogonal groups (ENGLISH)

#### Operator Algebra Seminars

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

Type II$_1$ von Neumann representations for Hecke operators on Maass forms (after F. Radulescu) (ENGLISH)

**Narutaka Ozawa**(Univ. Tokyo)Type II$_1$ von Neumann representations for Hecke operators on Maass forms (after F. Radulescu) (ENGLISH)

#### Seminar on Probability and Statistics

15:00-16:10 Room #000 (Graduate School of Math. Sci. Bldg.)

Mighty convergence in LAD type estimation (JAPANESE)

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/04.html

**MASUDA, Hiroki**(Graduate School of Mathematics, Kyushu University)Mighty convergence in LAD type estimation (JAPANESE)

[ Abstract ]

We propose a LAD (least absolute deviation) type contrast function for estimating Levy driven Ornstein-Uhlenbeck processes sampled at high frequency. The asymptotic behavior and polynomial-type large deviation inequality concerning the statistical random fields in question are derived, entailing an asymptotic normality and convergence of moments of the LAD estimator. Also, we will mention some numerical experiments done by the R software and some possible extensions of the framework.

[ Reference URL ]We propose a LAD (least absolute deviation) type contrast function for estimating Levy driven Ornstein-Uhlenbeck processes sampled at high frequency. The asymptotic behavior and polynomial-type large deviation inequality concerning the statistical random fields in question are derived, entailing an asymptotic normality and convergence of moments of the LAD estimator. Also, we will mention some numerical experiments done by the R software and some possible extensions of the framework.

http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/04.html

### 2010/07/13

#### Tuesday Seminar on Topology

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

High Distance Knots in closed 3-manifolds (ENGLISH)

**Marion Moore**(University of California, Davis)High Distance Knots in closed 3-manifolds (ENGLISH)

[ Abstract ]

Let M be a closed 3-manifold with a given Heegaard splitting.

We show that after a single stabilization, some core of the

stabilized splitting has arbitrarily high distance with respect

to the splitting surface. This generalizes a result of Minsky,

Moriah, and Schleimer for knots in S^3. We also show that in the

complex of curves, handlebody sets are either coarsely distinct

or identical. We define the coarse mapping class group of a

Heeegaard splitting, and show that if (S,V,W) is a Heegaard

splitting of genus greater than or equal to 2, then the coarse

mapping class group of (S,V,W) is isomorphic to the mapping class

group of (S, V, W). This is joint work with Matt Rathbun.

Let M be a closed 3-manifold with a given Heegaard splitting.

We show that after a single stabilization, some core of the

stabilized splitting has arbitrarily high distance with respect

to the splitting surface. This generalizes a result of Minsky,

Moriah, and Schleimer for knots in S^3. We also show that in the

complex of curves, handlebody sets are either coarsely distinct

or identical. We define the coarse mapping class group of a

Heeegaard splitting, and show that if (S,V,W) is a Heegaard

splitting of genus greater than or equal to 2, then the coarse

mapping class group of (S,V,W) is isomorphic to the mapping class

group of (S, V, W). This is joint work with Matt Rathbun.

#### Tuesday Seminar of Analysis

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

On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)

**Carlos Villegas Blas**(Universidad Nacional Autonoma de Mexico)On a limiting eigenvalue distribution theorem for perturbations of the hydrogen atom (JAPANESE)

[ Abstract ]

Let H be the hydrogen atom Hamiltonian. We will show that

the operator H+P can have well defined clusters of eigenvalues

for a suitable perturbation P=f(h)Q where Q is a pseudo-differential

operator of order zero and f(h) is a small quantity depending of

the Planck's parameter h. We will show that the distribution of

eigenvalues in those clusters has a semi-classical limit involving

the averages of the principal symbol of Q along the classical orbits

of the Kepler problem.

Let H be the hydrogen atom Hamiltonian. We will show that

the operator H+P can have well defined clusters of eigenvalues

for a suitable perturbation P=f(h)Q where Q is a pseudo-differential

operator of order zero and f(h) is a small quantity depending of

the Planck's parameter h. We will show that the distribution of

eigenvalues in those clusters has a semi-classical limit involving

the averages of the principal symbol of Q along the classical orbits

of the Kepler problem.

### 2010/07/12

#### Seminar on Geometric Complex Analysis

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

The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)

**Yu KAWAKAMI**(Kyushu Univ.)The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Flips of moduli of stable torsion free sheaves with $c_1=1$ on

$\\mathbb{P}^2$ (JAPANESE)

**Ryo Ohkawa**(Tokyo Institute of Technology)Flips of moduli of stable torsion free sheaves with $c_1=1$ on

$\\mathbb{P}^2$ (JAPANESE)

[ Abstract ]

We study flips of moduli schemes of stable torsion free sheaves

on the projective plane via wall-crossing phenomena of Bridgeland stability.

They are described as stratified Grassmann bundles by variation of

stability of modules over certain finite dimensional algebra.

We study flips of moduli schemes of stable torsion free sheaves

on the projective plane via wall-crossing phenomena of Bridgeland stability.

They are described as stratified Grassmann bundles by variation of

stability of modules over certain finite dimensional algebra.

### 2010/07/08

#### Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Effect of nonlinearity on the steady motion of a twinning dislocation (ENGLISH)

**Anna Vainchtein**(University of Pittsburgh, Department of Mathematics)Effect of nonlinearity on the steady motion of a twinning dislocation (ENGLISH)

[ Abstract ]

We consider the steady motion of a twinning dislocation in a Frenkel-Kontorova lattice with a double-well substrate potential that has a non-degenerate spinodal region. Semi-analytical traveling wave solutions are constructed for the piecewise quadratic potential, and their stability and further effects of nonlinearity are investigated numerically. We show that the width of the spinodal region and the nonlinearity of the potential have a significant effect on the dislocation kinetics, resulting in stable steady motion in some low-velocity intervals and lower propagation stress. We also conjecture that a stable steady propagation must correspond to an increasing portion of the kinetic relation between the applied stress and dislocation velocity.

We consider the steady motion of a twinning dislocation in a Frenkel-Kontorova lattice with a double-well substrate potential that has a non-degenerate spinodal region. Semi-analytical traveling wave solutions are constructed for the piecewise quadratic potential, and their stability and further effects of nonlinearity are investigated numerically. We show that the width of the spinodal region and the nonlinearity of the potential have a significant effect on the dislocation kinetics, resulting in stable steady motion in some low-velocity intervals and lower propagation stress. We also conjecture that a stable steady propagation must correspond to an increasing portion of the kinetic relation between the applied stress and dislocation velocity.

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Killing weeds with annular multiplicities $*10$ via quadratic tangles (ENGLISH)

**Dave Penneys**(UC Berkeley)Killing weeds with annular multiplicities $*10$ via quadratic tangles (ENGLISH)

[ Abstract ]

In recent work with Morrison, Peters, and Snyder, we eliminate two

families of possible principal graphs with graph norms less than 5 using

techniques derived from Jones' work on quadratic tangles.

In recent work with Morrison, Peters, and Snyder, we eliminate two

families of possible principal graphs with graph norms less than 5 using

techniques derived from Jones' work on quadratic tangles.

### 2010/07/07

#### Seminar on Mathematics for various disciplines

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Instabilities of steps on a vicinal face induced by the

asymmetry of diffusion field. (JAPANESE)

**Masahide Sato**(Information Media Center, Kanazawa University)Instabilities of steps on a vicinal face induced by the

asymmetry of diffusion field. (JAPANESE)

#### GCOE Seminars

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

代用電荷法による多重連結領域の数値等角写像 (JAPANESE)

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

**天野 要**(愛媛大学大学院理工学研究科)代用電荷法による多重連結領域の数値等角写像 (JAPANESE)

[ Abstract ]

多重連結領域の等角写像では,平行スリット領域,円弧スリット領域,放射スリット領域,円弧スリット円板領域,円弧スリット円環領域という5種の正準スリット領域が広く知られている(Nehari, 1952).遡って,Koebe(1916)はこれらを含む39種の正準スリット領域を挙げている.近年,このような多重連結領域の問題が新たに注目されている.代用電荷法を適用して,このような様々な等角写像の表現が簡潔で精度の高い近似写像関数を簡単に構成することができる.ここでは,非有界な多重連結領域から(実軸となす角を任意に指定した一般的な)直線スリット領域と,円弧放射スリット(混在)領域への場合中心に,代用電荷法による多重連結領域の数値等角写像の方法を紹介する.

[ Reference URL ]多重連結領域の等角写像では,平行スリット領域,円弧スリット領域,放射スリット領域,円弧スリット円板領域,円弧スリット円環領域という5種の正準スリット領域が広く知られている(Nehari, 1952).遡って,Koebe(1916)はこれらを含む39種の正準スリット領域を挙げている.近年,このような多重連結領域の問題が新たに注目されている.代用電荷法を適用して,このような様々な等角写像の表現が簡潔で精度の高い近似写像関数を簡単に構成することができる.ここでは,非有界な多重連結領域から(実軸となす角を任意に指定した一般的な)直線スリット領域と,円弧放射スリット(混在)領域への場合中心に,代用電荷法による多重連結領域の数値等角写像の方法を紹介する.

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

#### Numerical Analysis Seminar

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

Numerical conformal mappings of multiply connected domains by the charge simulation method (JAPANESE)

[ Reference URL ]

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

**Kaname Amano**(Ehime University)Numerical conformal mappings of multiply connected domains by the charge simulation method (JAPANESE)

[ Reference URL ]

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

#### Number Theory Seminar

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On the stable reduction of $X_0(p^4)$ (JAPANESE)

**Takahiro Tsushima**(University of Tokyo)On the stable reduction of $X_0(p^4)$ (JAPANESE)

### 2010/07/06

#### Tuesday Seminar on Topology

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

On the cohomology of free and twisted loop spaces (JAPANESE)

**Akira Kono**(Kyoto University)On the cohomology of free and twisted loop spaces (JAPANESE)

[ Abstract ]

A natural extension of cohomology suspension to a free loop space is

constructed from the evaluation map and is shown to have a good

properties in cohomology calculation. This map is generalized to a

twisted loop space.

As an application, the cohomology of free and twisted loop space of

classifying spaces of compact Lie groups, including certain finite

Chevalley groups is calculated.

A natural extension of cohomology suspension to a free loop space is

constructed from the evaluation map and is shown to have a good

properties in cohomology calculation. This map is generalized to a

twisted loop space.

As an application, the cohomology of free and twisted loop space of

classifying spaces of compact Lie groups, including certain finite

Chevalley groups is calculated.

#### Operator Algebra Seminars

16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)

On the Existence of the Dynamics for Anharmonic Quantum Oscillator Systems (ENGLISH)

**Robert Sims**(Univ. Arizona)On the Existence of the Dynamics for Anharmonic Quantum Oscillator Systems (ENGLISH)

### 2010/07/05

#### Seminar on Geometric Complex Analysis

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

Expression of restricted volumes with current integration (JAPANESE)

**Shin-ichi MATSUMURA**(Univ. of Tokyo)Expression of restricted volumes with current integration (JAPANESE)

#### Algebraic Geometry Seminar

16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)

Rational curves on hypersurfaces (JAPANESE)

**Katsuhisa Furukawa**(Waseda University)Rational curves on hypersurfaces (JAPANESE)

[ Abstract ]

Our purpose is to study the family of smooth rational curves of degree $e$ lying on a hypersurface of degree $d$ in $\\mathbb{P}^n$, and to investigate properties of this family (e.g., dimension, smoothness, connectedness).

Our starting point is the research about the family of lines (i.e., $e = 1$), which was studied by W. Barth and A. Van de Ven over $\\mathbb{C}$, and by J. Koll\\'{a}r over an algebraically closed field of arbitrary characteristic.

For the degree $e > 1$, the family of rational curves was studied by J. Harris, M. Roth, and J. Starr over $\\mathbb{C}$ in the case of $d < (n+1)/2$.

In this talk, we study the family of rational curves in arbitrary characteristic under the assumption $e = 2,3$ and $d > 1$, or $e > 3$ and $d > 2e-4$.

Our purpose is to study the family of smooth rational curves of degree $e$ lying on a hypersurface of degree $d$ in $\\mathbb{P}^n$, and to investigate properties of this family (e.g., dimension, smoothness, connectedness).

Our starting point is the research about the family of lines (i.e., $e = 1$), which was studied by W. Barth and A. Van de Ven over $\\mathbb{C}$, and by J. Koll\\'{a}r over an algebraically closed field of arbitrary characteristic.

For the degree $e > 1$, the family of rational curves was studied by J. Harris, M. Roth, and J. Starr over $\\mathbb{C}$ in the case of $d < (n+1)/2$.

In this talk, we study the family of rational curves in arbitrary characteristic under the assumption $e = 2,3$ and $d > 1$, or $e > 3$ and $d > 2e-4$.

### 2010/07/02

#### Colloquium

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

Hausdorff dimension and measure of conformal fractals (JAPANESE)

**Mitsuhiro Shishikura**(Kyoto University)Hausdorff dimension and measure of conformal fractals (JAPANESE)

### 2010/06/29

#### Tuesday Seminar on Topology

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

Non-commutative Reidemeister torsion and Morse-Novikov theory (JAPANESE)

**Takahiro Kitayama**(The University of Tokyo)Non-commutative Reidemeister torsion and Morse-Novikov theory (JAPANESE)

[ Abstract ]

For a circle-valued Morse function of a closed oriented manifold, we

show that Reidemeister torsion over a non-commutative formal Laurent

polynomial ring equals the product of a certain non-commutative

Lefschetz-type zeta function and the algebraic torsion of the Novikov

complex over the ring. This gives a generalization of the results of

Hutchings-Lee and Pazhitnov on abelian coefficients. As a consequence we

obtain Morse theoretical and dynamical descriptions of the higher-order

Alexander polynomials.

For a circle-valued Morse function of a closed oriented manifold, we

show that Reidemeister torsion over a non-commutative formal Laurent

polynomial ring equals the product of a certain non-commutative

Lefschetz-type zeta function and the algebraic torsion of the Novikov

complex over the ring. This gives a generalization of the results of

Hutchings-Lee and Pazhitnov on abelian coefficients. As a consequence we

obtain Morse theoretical and dynamical descriptions of the higher-order

Alexander polynomials.

### 2010/06/28

#### Seminar on Geometric Complex Analysis

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

Total Q-curvature vanishes on integrable CR manifolds (ENGLISH)

**Kengo HIRACHI**(Univ. of Tokyo)Total Q-curvature vanishes on integrable CR manifolds (ENGLISH)

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