## Seminar information archive

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

### 2012/03/13

#### Colloquium

15:00-16:00 Room #050 (Graduate School of Math. Sci. Bldg.)

Problems and results on Hardy's Z-function (JAPANESE)

**Aleksandar Ivic**(University of Belgrade, the Serbian Academy of Science and Arts)Problems and results on Hardy's Z-function (JAPANESE)

[ Abstract ]

The title is self-explanatory: G.H. Hardy first used the function

$Z(t)$ to show that there are infinitely many zeta-zeros on the

critical line $\\Re s = 1/2$. In recent years there is a revived

interest in this function, with many results and open problems.

The title is self-explanatory: G.H. Hardy first used the function

$Z(t)$ to show that there are infinitely many zeta-zeros on the

critical line $\\Re s = 1/2$. In recent years there is a revived

interest in this function, with many results and open problems.

#### Mathematical Biology Seminar

14:00-15:00 Room #154 (Graduate School of Math. Sci. Bldg.)

On construction of Lyapunov functions and functionals (JAPANESE)

**Tsuyoshi Kajiwara**(Okayama University)On construction of Lyapunov functions and functionals (JAPANESE)

### 2012/03/09

#### Infinite Analysis Seminar Tokyo

13:30-14:30 Room #002 (Graduate School of Math. Sci. Bldg.)

On Hall algebra of complexes (JAPANESE)

**Shintarou Yanagida**(Kobe Univ.)On Hall algebra of complexes (JAPANESE)

[ Abstract ]

The topic of my talk is the Hall algebra of complexes,

which is recently introduced by T. Bridgeland.

I will discuss its properties and relation to

auto-equivalences of derived category.

If I have enough time,

I will also discuss the relation

of this Hall algebra to the so-called Ding-Iohara algebra.

The topic of my talk is the Hall algebra of complexes,

which is recently introduced by T. Bridgeland.

I will discuss its properties and relation to

auto-equivalences of derived category.

If I have enough time,

I will also discuss the relation

of this Hall algebra to the so-called Ding-Iohara algebra.

### 2012/03/07

#### GCOE Seminars

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Nonsmooth Optimization, Theory and Applications. (ENGLISH)

**Kazufumi Ito**(North Carolina State Univ.)Nonsmooth Optimization, Theory and Applications. (ENGLISH)

[ Abstract ]

We develop a Lagrange multiplier theory for Nonsmooth optimization, including $L^¥infty$ and $L^1$ optimizations, $¥ell^0$ (counting meric) and $L^0$ (Ekeland mertic), Binary and Mixed integer optimizations and Data mining. A multitude of important problems can be treated by our approach and numerical algorithms are developed based on the Lagrange multiplier theory.

We develop a Lagrange multiplier theory for Nonsmooth optimization, including $L^¥infty$ and $L^1$ optimizations, $¥ell^0$ (counting meric) and $L^0$ (Ekeland mertic), Binary and Mixed integer optimizations and Data mining. A multitude of important problems can be treated by our approach and numerical algorithms are developed based on the Lagrange multiplier theory.

### 2012/03/06

#### GCOE Seminars

16:00-17:00 Room #370 (Graduate School of Math. Sci. Bldg.)

On the phase field approach to shape and topology optimization (ENGLISH)

**Dietmar Hoemberg**(Weierstrass Institute, Berlin)On the phase field approach to shape and topology optimization (ENGLISH)

[ Abstract ]

Owing to different densities of the respective phases, solid-solid phase transitions often are accompanied by (often undesired) changes in workpiece size and shape. In my talk I will address the reverse question of finding an optimal phase mixture in order to accomplish a desired workpiece shape.

From mathematical point of view this corresponds to an optimal shape design problem subject to a static mechanical equilibrium problem with phase dependent stiffness tensor, in which the two phases exhibit different densities leading to different internal stresses. Our goal is to tackle this problem using a phasefield relaxation.

To this end we first briefly recall previous works regarding phasefield approaches to topology optimization (e.g. by Bourdin ¥& Chambolle, Burger ¥& Stainko and Blank, Garcke et al.).

We add a Ginzburg-Landau term to our cost functional, derive an adjoint equation for the displacement and choose a gradient flow dynamics with an articial time variable for our phasefield variable. We discuss well-posedness results for the resulting system and conclude with some numerical results.

Owing to different densities of the respective phases, solid-solid phase transitions often are accompanied by (often undesired) changes in workpiece size and shape. In my talk I will address the reverse question of finding an optimal phase mixture in order to accomplish a desired workpiece shape.

From mathematical point of view this corresponds to an optimal shape design problem subject to a static mechanical equilibrium problem with phase dependent stiffness tensor, in which the two phases exhibit different densities leading to different internal stresses. Our goal is to tackle this problem using a phasefield relaxation.

To this end we first briefly recall previous works regarding phasefield approaches to topology optimization (e.g. by Bourdin ¥& Chambolle, Burger ¥& Stainko and Blank, Garcke et al.).

We add a Ginzburg-Landau term to our cost functional, derive an adjoint equation for the displacement and choose a gradient flow dynamics with an articial time variable for our phasefield variable. We discuss well-posedness results for the resulting system and conclude with some numerical results.

#### GCOE Seminars

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Finite element simulations of induction hardening of steel parts (ENGLISH)

**Thomas Petzold**(Weierstrass Institute, Berlin)Finite element simulations of induction hardening of steel parts (ENGLISH)

[ Abstract ]

Induction hardening is a modern method for the heat treatment of steel parts.

A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer.

The process is very fast and energy efficient and plays a big role in modern manufacturing facilities in many industrial application areas.

In this talk a model for induction hardening of steel parts is presented. It consist of a system of partial differential equations including Maxwell's equations and the heat equation.

The finite element method is used to perform numerical simulations in 3D.

This requires a suitable discretization of Maxwell's equations leading to so called edge-finite-elements.

We will give a short overview of edge elements and present numerical simulations of induction hardening.

We will address some of the difficulties arising when solving the large system of non-linear coupled PDEs in three space dimensions.

Induction hardening is a modern method for the heat treatment of steel parts.

A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer.

The process is very fast and energy efficient and plays a big role in modern manufacturing facilities in many industrial application areas.

In this talk a model for induction hardening of steel parts is presented. It consist of a system of partial differential equations including Maxwell's equations and the heat equation.

The finite element method is used to perform numerical simulations in 3D.

This requires a suitable discretization of Maxwell's equations leading to so called edge-finite-elements.

We will give a short overview of edge elements and present numerical simulations of induction hardening.

We will address some of the difficulties arising when solving the large system of non-linear coupled PDEs in three space dimensions.

### 2012/02/29

#### GCOE Seminars

16:00-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Direct and inverse scattering of elastic waves by diffraction gratings (ENGLISH)

**Johannes Elschner**(Weierstrass Institute, Germany)Direct and inverse scattering of elastic waves by diffraction gratings (ENGLISH)

[ Abstract ]

The talk presents joint work with Guanghui Hu on the scattering of time-harmonic plane elastic waves by two-dimensional periodic structures. The first part presents existence and uniqueness results for the direct problem , using a variational approach. For the inverse problem, we discuss global uniqueness results with a minimal number of incident pressure or shear waves under the boundary conditions of the third and fourth kind. Generalizations to biperiodic elastic diffraction gratings in 3D are also mentioned. Finally we consider a reconstruction method applied to the inverse Dirichlet problem for the quasi-periodic 2D Navier equation.

The talk presents joint work with Guanghui Hu on the scattering of time-harmonic plane elastic waves by two-dimensional periodic structures. The first part presents existence and uniqueness results for the direct problem , using a variational approach. For the inverse problem, we discuss global uniqueness results with a minimal number of incident pressure or shear waves under the boundary conditions of the third and fourth kind. Generalizations to biperiodic elastic diffraction gratings in 3D are also mentioned. Finally we consider a reconstruction method applied to the inverse Dirichlet problem for the quasi-periodic 2D Navier equation.

### 2012/02/22

#### Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Twistor $D$-module and harmonic bundle (ENGLISH)

**Takuro Mochizuki**(Research Institute for Mathematical Sciences, Kyoto University)Twistor $D$-module and harmonic bundle (ENGLISH)

[ Abstract ]

Abstract:

We shall overview the theory of twistor $D$-modules and

harmonic bundles. I am planning to survey the following topics,

motivated by the Hard Lefschetz Theorem for semisimple holonomic

$D$-modules:

1. What is a twistor $D$-module?

2. Local structure of meromorphic flat bundles

3. Wild harmonic bundles from local and global viewpoints

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

Abstract:

We shall overview the theory of twistor $D$-modules and

harmonic bundles. I am planning to survey the following topics,

motivated by the Hard Lefschetz Theorem for semisimple holonomic

$D$-modules:

1. What is a twistor $D$-module?

2. Local structure of meromorphic flat bundles

3. Wild harmonic bundles from local and global viewpoints

(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)

#### GCOE Seminars

15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)

Justification of a Shallow Shell Model in Unilateral Contact with an Obstacle (ENGLISH)

**Bernadette Miara**(Université Paris-Est, ESIEE, France)Justification of a Shallow Shell Model in Unilateral Contact with an Obstacle (ENGLISH)

[ Abstract ]

We consider a three-dimensional elastic shell in unilateral contact with a plane. This lecture aims at justifying the asymptotic limit of the set of equilibrium equations of the structure when the thickness of the shell goes to zero. More precisely, we start with the 3D Signorini problem (with finite thickness) and obtain at the limit an obstacle 2D problem. This problem has already been studied [4] in the Cartesian framework on the basis of the bi-lateral problem [3]. The interest and the difficulty of the approach in the curvilinear framework (more appropriate to handle general shells) is due to the coupling between the tangential and transverse covariant components of the elastic field in the expression of the nonpenetrability conditions.

The procedure is the same as the one used in the asymptotic analysis of 3D bilateral structures [1, 2]: assumptions on the data, (loads and geometry of the middle surface of the shell) and re-scalling of the unknowns (displacement field or stress tensor); the new feature is the special handling of the components coupling.

The main result we obtain is as follows:

i) Under the assumption of regularity of the external volume and surface loads, and of the mapping that defines the middle surface of the shell, we establish that the family of elastic displacements converges strongly as the thickness tends to zero in an appropriate set which is a convex cone.

ii) The limit elastic displacement is a Kirchhoff-Love field given by a variational problem which will be analysed into details. The contact conditions are fully explicited for any finite thickness and at the limit.

This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.

We consider a three-dimensional elastic shell in unilateral contact with a plane. This lecture aims at justifying the asymptotic limit of the set of equilibrium equations of the structure when the thickness of the shell goes to zero. More precisely, we start with the 3D Signorini problem (with finite thickness) and obtain at the limit an obstacle 2D problem. This problem has already been studied [4] in the Cartesian framework on the basis of the bi-lateral problem [3]. The interest and the difficulty of the approach in the curvilinear framework (more appropriate to handle general shells) is due to the coupling between the tangential and transverse covariant components of the elastic field in the expression of the nonpenetrability conditions.

The procedure is the same as the one used in the asymptotic analysis of 3D bilateral structures [1, 2]: assumptions on the data, (loads and geometry of the middle surface of the shell) and re-scalling of the unknowns (displacement field or stress tensor); the new feature is the special handling of the components coupling.

The main result we obtain is as follows:

i) Under the assumption of regularity of the external volume and surface loads, and of the mapping that defines the middle surface of the shell, we establish that the family of elastic displacements converges strongly as the thickness tends to zero in an appropriate set which is a convex cone.

ii) The limit elastic displacement is a Kirchhoff-Love field given by a variational problem which will be analysed into details. The contact conditions are fully explicited for any finite thickness and at the limit.

This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.

#### GCOE Seminars

16:15-17:15 Room #270 (Graduate School of Math. Sci. Bldg.)

Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data. (ENGLISH)

**Oleg Emanouilov**(Colorado State University)Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data. (ENGLISH)

[ Abstract ]

In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.

Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data

$$

{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\\\\tilde Gamma}¥vert

- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}

$$

where $¥tilde ¥Gamma$ is an arbitrary fixed open set of

$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.

In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.

Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data

$$

{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\\\\tilde Gamma}¥vert

- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}

$$

where $¥tilde ¥Gamma$ is an arbitrary fixed open set of

$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.

### 2012/02/21

#### Tuesday Seminar on Topology

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

Property (TT)/T and homomorphism superrigidity into mapping class groups (JAPANESE)

**Masato Mimura**(The University of Tokyo)Property (TT)/T and homomorphism superrigidity into mapping class groups (JAPANESE)

[ Abstract ]

Mapping class groups (MCG's), of compact oriented surfaces (possibly

with punctures), have many mysterious features: they behave not only

like higher rank lattices (namely, irreducible lattices in higher rank

algebraic groups); but also like rank one lattices. The following

theorem, the Farb--Kaimanovich--Masur superrigidity, states a rank one

phenomenon for MCG's: "every group homomorphism from higher rank

lattices (such as SL(3,Z) and cocompact lattices in SL(3,R)) into

MCG's has finite image."

In this talk, we show a generalization of the superrigidity above, to

the case where higher rank lattices are replaced with some

(non-arithmetic) matrix groups over general rings. Our main example of

such groups is called the "universal lattice", that is, the special

linear group over commutative finitely generated polynomial rings over

integers, (such as SL(3,Z[x])). To prove this, we introduce the notion

of "property (TT)/T" for groups, which is a strengthening of Kazhdan's

property (T).

We will explain these properties and relations to ordinary and bounded

cohomology of groups (with twisted unitary coefficients); and outline

the proof of our result.

Mapping class groups (MCG's), of compact oriented surfaces (possibly

with punctures), have many mysterious features: they behave not only

like higher rank lattices (namely, irreducible lattices in higher rank

algebraic groups); but also like rank one lattices. The following

theorem, the Farb--Kaimanovich--Masur superrigidity, states a rank one

phenomenon for MCG's: "every group homomorphism from higher rank

lattices (such as SL(3,Z) and cocompact lattices in SL(3,R)) into

MCG's has finite image."

In this talk, we show a generalization of the superrigidity above, to

the case where higher rank lattices are replaced with some

(non-arithmetic) matrix groups over general rings. Our main example of

such groups is called the "universal lattice", that is, the special

linear group over commutative finitely generated polynomial rings over

integers, (such as SL(3,Z[x])). To prove this, we introduce the notion

of "property (TT)/T" for groups, which is a strengthening of Kazhdan's

property (T).

We will explain these properties and relations to ordinary and bounded

cohomology of groups (with twisted unitary coefficients); and outline

the proof of our result.

### 2012/02/20

#### Functional Analysis Seminar

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

Microscopic derivation of the Ginzburg-Landau model (ENGLISH)

**Jan Philip SOLOVEJ**(University of Copenhagen)Microscopic derivation of the Ginzburg-Landau model (ENGLISH)

[ Abstract ]

I will discuss how the \\emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.

I will discuss how the \\emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.

### 2012/02/14

#### Tuesday Seminar of Analysis

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

Symmetry results for Caffarelli-Kohn-Nirenberg inequalities (ENGLISH)

**Michael Loss**(Georgia Institute of Technology)Symmetry results for Caffarelli-Kohn-Nirenberg inequalities (ENGLISH)

### 2012/02/07

#### GCOE Seminars

14:00-15:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Controllability results for degenerate parabolic operators (ENGLISH)

**Piermarco Cannarsa**(Mat. Univ. Roma "Tor Vergata")Controllability results for degenerate parabolic operators (ENGLISH)

[ Abstract ]

UnlikeCuniformly parabolic equations, parabolic operators that degenerate on subsets of the space domain exhibit very different behaviors from the point of view of controllability. For instance, null controllability in arbitrary time may be true or false according to the degree of degeneracy, and there are also examples where a finite time is needed to ensure such a property. This talk will survey most of the theory that has been established so far for operators with boundary degeneracy, and discuss recent results for operators of Grushin type which degenerate in the interior.

UnlikeCuniformly parabolic equations, parabolic operators that degenerate on subsets of the space domain exhibit very different behaviors from the point of view of controllability. For instance, null controllability in arbitrary time may be true or false according to the degree of degeneracy, and there are also examples where a finite time is needed to ensure such a property. This talk will survey most of the theory that has been established so far for operators with boundary degeneracy, and discuss recent results for operators of Grushin type which degenerate in the interior.

### 2012/02/03

#### thesis presentations

09:45-11:00 Room #118 (Graduate School of Math. Sci. Bldg.)

How to estimate Seshadri constants(セシャドリ定数を評価する方法)

(JAPANESE)

**Atsushi ITO**(Graduate School of Mathematical Sciences University of Tokyo)How to estimate Seshadri constants(セシャドリ定数を評価する方法)

(JAPANESE)

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Spherical functions associated to the principal series representations of SL(3,R) and higher rank Epstein zeta functions(SL(3,R)の主系列表現に付随する球関数,及び高階Epsteinゼータ関数について)

(JAPANESE)

**Keijyu SONO**(Graduate School of Mathematical Sciences University of Tokyo)Spherical functions associated to the principal series representations of SL(3,R) and higher rank Epstein zeta functions(SL(3,R)の主系列表現に付随する球関数,及び高階Epsteinゼータ関数について)

(JAPANESE)

#### thesis presentations

13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Construction of invariant group orderings from topological point of view(位相幾何の視点からの群の不変順序の構成)

(JAPANESE)

**Tetsuya ITO**(Graduate School of Mathematical Sciences University of Tokyo)Construction of invariant group orderings from topological point of view(位相幾何の視点からの群の不変順序の構成)

(JAPANESE)

#### thesis presentations

14:15-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)

The explicit calculation of Čech cohomology and an extension of Davenport’s inequality(Čechコホモロジーの明示的計算とDavenport不等式の拡張)

(JAPANESE)

**TIAN Ran**(Graduate School of Mathematical Sciences University of Tokyo)The explicit calculation of Čech cohomology and an extension of Davenport’s inequality(Čechコホモロジーの明示的計算とDavenport不等式の拡張)

(JAPANESE)

#### thesis presentations

09:45-11:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Hybridized Discontinuous Galerkin Methods for Elliptic Problems(楕円型問題に対するハイブリッド型不連続ガレルキン法の研究)

(JAPANESE)

**Issei OIKAWA**(Graduate School of Mathematical Sciences University of Tokyo)Hybridized Discontinuous Galerkin Methods for Elliptic Problems(楕円型問題に対するハイブリッド型不連続ガレルキン法の研究)

(JAPANESE)

#### thesis presentations

11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Two-dimensional stochastic Navier-Stokes equations derived from a certain variational problem(ある変分問題から導かれる二次元確率ナビエ・ストークス方程式)

(JAPANESE)

**Satoshi YOKOYAMA**(Graduate School of Mathematical Sciences University of Tokyo)Two-dimensional stochastic Navier-Stokes equations derived from a certain variational problem(ある変分問題から導かれる二次元確率ナビエ・ストークス方程式)

(JAPANESE)

#### thesis presentations

13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Scattering Theory on Manifolds with Asympotically Polynomially Growing Ends(多項式増大する無限遠境界を持つ多様体上の散乱理論)

(JAPANESE)

**Shinichiro ITOZAKI**(Graduate School of Mathematical Sciences University of Tokyo)Scattering Theory on Manifolds with Asympotically Polynomially Growing Ends(多項式増大する無限遠境界を持つ多様体上の散乱理論)

(JAPANESE)

#### thesis presentations

14:15-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)

On the exact WKB analysis of Schrödinger equations(Schrödinger方程式の完全WKB解析に関して)

(JAPANESE)

**Shingo KAMIMOTO**(Graduate School of Mathematical Sciences University of Tokyo)On the exact WKB analysis of Schrödinger equations(Schrödinger方程式の完全WKB解析に関して)

(JAPANESE)

### 2012/02/02

#### Operator Algebra Seminars

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

Weak Exactness for $C^*$-algebras and Application to Condition (AO) (JAPANESE)

**Yusuke Isono**(Univ. Tokyo)Weak Exactness for $C^*$-algebras and Application to Condition (AO) (JAPANESE)

#### thesis presentations

11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Studies on the geometry of Mori dream spaces(森夢空間の幾何学に関する研究) (JAPANESE)

**Shinnosuke OKAWA**(Graduate School of Mathematical Sciences University of Tokyo )Studies on the geometry of Mori dream spaces(森夢空間の幾何学に関する研究) (JAPANESE)

#### thesis presentations

13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)

The p-adic monodromy theorem in the imperfect residue field case(剰余体が非完全な場合のp進モノドロミー定理について)

(JAPANESE)

**Shun OKUBO**(Graduate School of Mathematical Sciences University of Tokyo)The p-adic monodromy theorem in the imperfect residue field case(剰余体が非完全な場合のp進モノドロミー定理について)

(JAPANESE)

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