## Seminar information archive

Seminar information archive ～02/06｜Today's seminar 02/07 | Future seminars 02/08～

#### thesis presentations

15:45-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Conditional stability by Carleman estimates for inverse problems : coefficient inverse problems for the Dirac equation, the determination of subboundary by the heat equation and the continuation of solution of the Euler equation(逆問題に対するカーレマン評価による条件付き安定性: ディラック方程式に対する係数逆問題,熱方程式による部分境界の決定とオイラー方程式に対する解の接続性) (JAPANESE)

**Atsushi KAWAMOTO**(Graduate School of Mathematical Sciences University of Tokyo)Conditional stability by Carleman estimates for inverse problems : coefficient inverse problems for the Dirac equation, the determination of subboundary by the heat equation and the continuation of solution of the Euler equation(逆問題に対するカーレマン評価による条件付き安定性: ディラック方程式に対する係数逆問題,熱方程式による部分境界の決定とオイラー方程式に対する解の接続性) (JAPANESE)

### 2011/02/02

#### Lectures

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

Connectedness of a level set and a generalization of Oleinik and Aronson-Benilan type one-sided inequalities (ENGLISH)

**Yong Jung Kim**(Korea Advanced Institute of Science and Technology (KAIST))Connectedness of a level set and a generalization of Oleinik and Aronson-Benilan type one-sided inequalities (ENGLISH)

[ Abstract ]

The one-sided Oleinik inequality provides the uniqueness and a sharp regularity of solutions to a scalar conservation law. The Aronson-Benilan type one-sided inequalities also play a similar role. We will discuss about their generalization to a general setting.

The one-sided Oleinik inequality provides the uniqueness and a sharp regularity of solutions to a scalar conservation law. The Aronson-Benilan type one-sided inequalities also play a similar role. We will discuss about their generalization to a general setting.

#### Lectures

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

Regularity of two dimensional capillary gravity water waves (ENGLISH)

**Guanghui ZHANG**(Graduate School of Mathematical Sciences, the University of Tokyo)Regularity of two dimensional capillary gravity water waves (ENGLISH)

[ Abstract ]

We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. This is a joint work with Georg Weiss.

We consider the two-dimensional steady capillary water waves with vorticity. In the case of zero surface tension, it is well known that the free surface of a wave of maximal amplitude is not smooth at a free surface point of maximal height, but forms a sharp crest with an angle of 120 degrees. When the surface tension is not zero, physical intuition suggests that the corner singularities should disappear. In this talk we prove that for suitable weak solutions, the free surfaces are smooth. On a technical level, solutions of our problem are closely related to critical points of the Mumford-Shah functional, so that our main task is to exclude cusps pointing into the water phase. This is a joint work with Georg Weiss.

#### Seminar on Probability and Statistics

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

An Attempt to formalize Statistical Inferences for Weakly Dependent Time-Series Data and Some Trials for Statistical Analysis of Financial Data (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/08.html

**MIURA, Ryozo**(Hitotsubashi University)An Attempt to formalize Statistical Inferences for Weakly Dependent Time-Series Data and Some Trials for Statistical Analysis of Financial Data (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/08.html

### 2011/01/31

#### Algebraic Geometry Seminar

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

Restriction maps to the Coble quartic (ENGLISH)

**Sukmoon Huh**(KIAS)Restriction maps to the Coble quartic (ENGLISH)

[ Abstract ]

The Coble sixfold quartic is the moduli space of semi-stable vector bundle of rank 2 on a non-hyperelliptic curve of genus 3 with canonical determinant. Considering the curve as a plane quartic, we investigate the restriction of the semi-stable sheaves over the projective plane to the curve. We suggest a positive side of this trick in the study of the moduli space of vector bundles over curves by showing several examples such as Brill-Noether loci and a few rational subvarieties of the Coble quartic. In a later part of the talk, we introduce the rationality problem of the Coble quartic. If the time permits, we will apply the same idea to the moduli space of bundles over curves of genus 4 to derive some geometric properties of the Brill-Noether loci in the case of genus 4.

The Coble sixfold quartic is the moduli space of semi-stable vector bundle of rank 2 on a non-hyperelliptic curve of genus 3 with canonical determinant. Considering the curve as a plane quartic, we investigate the restriction of the semi-stable sheaves over the projective plane to the curve. We suggest a positive side of this trick in the study of the moduli space of vector bundles over curves by showing several examples such as Brill-Noether loci and a few rational subvarieties of the Coble quartic. In a later part of the talk, we introduce the rationality problem of the Coble quartic. If the time permits, we will apply the same idea to the moduli space of bundles over curves of genus 4 to derive some geometric properties of the Brill-Noether loci in the case of genus 4.

#### Kavli IPMU Komaba Seminar

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

Mirror symmetry for toric Calabi-Yau manifolds from the SYZ viewpoint (ENGLISH)

**Kwok-Wai Chan**(IPMU, the University of Tokyo)Mirror symmetry for toric Calabi-Yau manifolds from the SYZ viewpoint (ENGLISH)

[ Abstract ]

In this talk, I will discuss mirror symmetry for toric

Calabi-Yau (CY) manifolds from the viewpoint of the SYZ program. I will

start with a special Lagrangian torus fibration on a toric CY manifold,

and then construct its instanton-corrected mirror by a T-duality modified

by quantum corrections. A remarkable feature of this construction is that

the mirror family is inherently written in canonical flat coordinates. As

a consequence, we get a conjectural enumerative meaning for the inverse

mirror maps. If time permits, I will explain the verification of this

conjecture in several examples via a formula which computes open

Gromov-Witten invariants for toric manifolds.

In this talk, I will discuss mirror symmetry for toric

Calabi-Yau (CY) manifolds from the viewpoint of the SYZ program. I will

start with a special Lagrangian torus fibration on a toric CY manifold,

and then construct its instanton-corrected mirror by a T-duality modified

by quantum corrections. A remarkable feature of this construction is that

the mirror family is inherently written in canonical flat coordinates. As

a consequence, we get a conjectural enumerative meaning for the inverse

mirror maps. If time permits, I will explain the verification of this

conjecture in several examples via a formula which computes open

Gromov-Witten invariants for toric manifolds.

#### Seminar on Geometric Complex Analysis

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

Varieties with ample cotangent bundle and hyperbolicity (ENGLISH)

**Damian Brotbek**(Rennes Univ.)Varieties with ample cotangent bundle and hyperbolicity (ENGLISH)

[ Abstract ]

Varieties with ample cotangent bundle satisfy many interesting properties and are supposed to be abundant, however relatively few concrete examples are known. In this talk we will construct such examples as complete intersection surfaces in projective space, and explain how this problem is related to the study of hyperbolicity properties for hypersurfaces.

Varieties with ample cotangent bundle satisfy many interesting properties and are supposed to be abundant, however relatively few concrete examples are known. In this talk we will construct such examples as complete intersection surfaces in projective space, and explain how this problem is related to the study of hyperbolicity properties for hypersurfaces.

### 2011/01/28

#### Colloquium

16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)

Conformal invariance in probability theory (JAPANESE)

**Shirai Tomoyuki**(Kyushu University)Conformal invariance in probability theory (JAPANESE)

#### Operator Algebra Seminars

14:45-16:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Semiprojectivity of graph algebras (ENGLISH)

**Takeshi Katsura**(Keio University)Semiprojectivity of graph algebras (ENGLISH)

### 2011/01/27

#### Operator Algebra Seminars

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

Entire Cyclic Cohomology of Noncommutative Riemann Surfaces (JAPANESE)

**Hiroshi Takai**(Tokyo Metropolitan University)Entire Cyclic Cohomology of Noncommutative Riemann Surfaces (JAPANESE)

#### Applied Analysis

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

Attraction at infinity: Constructing non-compact global attractors in the slowly non-dissipative realm (ENGLISH)

**Nitsan Ben-Gal**(The Weizmann Institute of Science)Attraction at infinity: Constructing non-compact global attractors in the slowly non-dissipative realm (ENGLISH)

[ Abstract ]

One of the primary tools for understanding the much-studied realm of reaction-diffusion equations is the global attractor, which provides us with a qualitative understanding of the governing behaviors of solutions to the equation in question. Nevertheless, the classic global attractor for such systems is defined to be compact, and thus attractor theory has previously excluded such analysis from being applied to non-dissipative reaction-diffusion equations.

In this talk I will present recent results in which I developed a non-compact analogue to the classical global attractor, and will discuss the methods derived in order to obtain a full decomposition of the non-compact global attractor for a slowly non-dissipative reaction-diffusion equation. In particular, attention will be paid to the nodal property techniques and reduction methods which form a critical underpinning of asymptotics research in both dissipative and non-dissipative evolutionary equations. I will discuss the concepts of the ‘completed inertial manifold’ and ‘non-compact global attractor’, and show how these in particular allow us to produce equivalent results for a class of slowly non-dissipative equations as have been achieved for dissipative equations. Additionally, I will address the behavior of solutions to slowly non-dissipative equations approaching and at infinity, the realm which presents both the challenges and rewards of removing the necessity of dissipativity.

One of the primary tools for understanding the much-studied realm of reaction-diffusion equations is the global attractor, which provides us with a qualitative understanding of the governing behaviors of solutions to the equation in question. Nevertheless, the classic global attractor for such systems is defined to be compact, and thus attractor theory has previously excluded such analysis from being applied to non-dissipative reaction-diffusion equations.

In this talk I will present recent results in which I developed a non-compact analogue to the classical global attractor, and will discuss the methods derived in order to obtain a full decomposition of the non-compact global attractor for a slowly non-dissipative reaction-diffusion equation. In particular, attention will be paid to the nodal property techniques and reduction methods which form a critical underpinning of asymptotics research in both dissipative and non-dissipative evolutionary equations. I will discuss the concepts of the ‘completed inertial manifold’ and ‘non-compact global attractor’, and show how these in particular allow us to produce equivalent results for a class of slowly non-dissipative equations as have been achieved for dissipative equations. Additionally, I will address the behavior of solutions to slowly non-dissipative equations approaching and at infinity, the realm which presents both the challenges and rewards of removing the necessity of dissipativity.

### 2011/01/26

#### Number Theory Seminar

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

The p-adic Gross-Zagier formula for elliptic curves at supersingular primes (JAPANESE)

**Shinichi Kobayashi**(Tohoku University)The p-adic Gross-Zagier formula for elliptic curves at supersingular primes (JAPANESE)

[ Abstract ]

The p-adic Gross-Zagier formula is a formula relating the derivative of the p-adic L-function of elliptic curves to the p-adic height of Heegner points. For a good ordinary prime p, the formula is proved by B. Perrin-Riou more than 20 years ago. Recently, the speaker proved it for a supersingular prime p. In this talk, he explains the proof.

The p-adic Gross-Zagier formula is a formula relating the derivative of the p-adic L-function of elliptic curves to the p-adic height of Heegner points. For a good ordinary prime p, the formula is proved by B. Perrin-Riou more than 20 years ago. Recently, the speaker proved it for a supersingular prime p. In this talk, he explains the proof.

#### PDE Real Analysis Seminar

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

)

Quenching Problem Arising in Micro-electro Mechanical Systems

(JAPANESE)

**Jong-Shenq Guo**(Department of Mathematics, Tamkang University)

Quenching Problem Arising in Micro-electro Mechanical Systems

(JAPANESE)

[ Abstract ]

In this talk, we shall present some recent results on quenching problems which arise in Micro-electro Mechanical Systems.

We shall also give some open problems in this research area.

In this talk, we shall present some recent results on quenching problems which arise in Micro-electro Mechanical Systems.

We shall also give some open problems in this research area.

#### Seminar on Probability and Statistics

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

Semi-parametric profile likelihood estimation and implicitly defined functions (JAPANESE)

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/07.html

**HIROSE, Yuichi**(Victoria University of Wellington)Semi-parametric profile likelihood estimation and implicitly defined functions (JAPANESE)

[ Abstract ]

The object of talk is the differentiability of implicitly defined functions which we

encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild

(1997, 2001) and Murphy and Vaart (2000) developed methodologies that can avoid dealing with such implicitly

defined functions by reparametrizing parameters in the profile likelihood and using an approximate least

favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach

developed in Hirose (2010) which uses the differentiability of implicitly defined functions.

[ Reference URL ]The object of talk is the differentiability of implicitly defined functions which we

encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild

(1997, 2001) and Murphy and Vaart (2000) developed methodologies that can avoid dealing with such implicitly

defined functions by reparametrizing parameters in the profile likelihood and using an approximate least

favorable submodel in semi-parametric models. Our result shows applicability of an alternative approach

developed in Hirose (2010) which uses the differentiability of implicitly defined functions.

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/07.html

### 2011/01/25

#### Tuesday Seminar on Topology

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

On unknotting of surface-knots with small sheet numbers

(JAPANESE)

**Chikara Haruta**(Graduate School of Mathematical Sciences, the University of Tokyo )On unknotting of surface-knots with small sheet numbers

(JAPANESE)

[ Abstract ]

A connected surface smoothly embedded in ${\\mathbb R}^4$ is called a surface-knot. In particular, if a surface-knot $F$ is homeomorphic to the $2$-sphere or the torus, then it is called an $S^2$-knot or a $T^2$-knot, respectively. The sheet number of a surface-knot is an invariant analogous to the crossing number of a $1$-knot. M. Saito and S. Satoh proved some results concerning the sheet number of an $S^2$-knot. In particular, it is known that an $S^2$-knot is trivial if and only if its sheet number is $1$, and there is no $S^2$-knot whose sheet number is $2$. In this talk, we show that there is no $S^2$-knot whose sheet number is $3$, and a $T^2$-knot is trivial if and only if its sheet number is $1$.

A connected surface smoothly embedded in ${\\mathbb R}^4$ is called a surface-knot. In particular, if a surface-knot $F$ is homeomorphic to the $2$-sphere or the torus, then it is called an $S^2$-knot or a $T^2$-knot, respectively. The sheet number of a surface-knot is an invariant analogous to the crossing number of a $1$-knot. M. Saito and S. Satoh proved some results concerning the sheet number of an $S^2$-knot. In particular, it is known that an $S^2$-knot is trivial if and only if its sheet number is $1$, and there is no $S^2$-knot whose sheet number is $2$. In this talk, we show that there is no $S^2$-knot whose sheet number is $3$, and a $T^2$-knot is trivial if and only if its sheet number is $1$.

### 2011/01/24

#### Seminar on Geometric Complex Analysis

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

Toward a complex analytic 3-dimensional Kleinian group theory (JAPANESE)

**Masahide Kato**(Sophia Univ.)Toward a complex analytic 3-dimensional Kleinian group theory (JAPANESE)

### 2011/01/20

#### Operator Algebra Seminars

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

Property (TT)/T and homomorphism rigidity into Out$(F_n)$ (JAPANESE)

**Masato Mimura**(Univ. Tokyo)Property (TT)/T and homomorphism rigidity into Out$(F_n)$ (JAPANESE)

### 2011/01/19

#### Seminar on Mathematics for various disciplines

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

Exploration of essence of Mullins equation (JAPANESE)

**Yoshihito Ogasawara**(Waseda University Faculty of Science and Engineering)Exploration of essence of Mullins equation (JAPANESE)

#### Seminar on Probability and Statistics

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

Notes on estimating the probability of ruin and some generalization (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/06.html

**SHIMIZU, Yasutaka**(Osaka University)Notes on estimating the probability of ruin and some generalization (JAPANESE)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/06.html

### 2011/01/18

#### Operator Algebra Seminars

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

Scattering induced current in a tight binding band (ENGLISH)

**Claude-Alain Pillet**(Univ. de Toulon et du Var)Scattering induced current in a tight binding band (ENGLISH)

#### Lie Groups and Representation Theory

17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Connections between Noncommutative Geometry and Lie groups

representations (ENGLISH)

**Pierre Clare**(Universite Orleans and the University of Tokyo)Connections between Noncommutative Geometry and Lie groups

representations (ENGLISH)

[ Abstract ]

One of the principles of Noncommutative Geometry is to study singular spaces that the tools of classical analysis like algebras of continuous functions fail to describe, replacing them by more general C*-algebras. After recalling fundamental facts about C*-algebras, Hilbert modules and group C*-algebras, we will present constructions and results aiming to understand principal series representations and Knapp-Stein theory in the noncommutative geometrical framework. Eventually we will explain the relationship between the analysis of reduced group C*-algebras and the computation of the Connes-Kasparov isomorphisms.

One of the principles of Noncommutative Geometry is to study singular spaces that the tools of classical analysis like algebras of continuous functions fail to describe, replacing them by more general C*-algebras. After recalling fundamental facts about C*-algebras, Hilbert modules and group C*-algebras, we will present constructions and results aiming to understand principal series representations and Knapp-Stein theory in the noncommutative geometrical framework. Eventually we will explain the relationship between the analysis of reduced group C*-algebras and the computation of the Connes-Kasparov isomorphisms.

### 2011/01/17

#### Algebraic Geometry Seminar

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

L^2 methods and Skoda division theorems (ENGLISH)

**Dano Kim**(KIAS)L^2 methods and Skoda division theorems (ENGLISH)

[ Abstract ]

Extension of Ohsawa-Takegoshi type and division of Skoda type are two important consequences of the L^2 methods of Hormander, Demailly and others. They are analogous to vanishing theorems of Kodaira type and can be viewed as some refinement of the vanishing. The best illustration of their usefulness up to now is Siu’s proof of invariance of plurigenera without general type assumption. In this talk, we will focus on the division theorem / problem and talk about its currently known cases (old and new). One motivation comes from yet another viewpoint on the finite generation of canonical ring.

Extension of Ohsawa-Takegoshi type and division of Skoda type are two important consequences of the L^2 methods of Hormander, Demailly and others. They are analogous to vanishing theorems of Kodaira type and can be viewed as some refinement of the vanishing. The best illustration of their usefulness up to now is Siu’s proof of invariance of plurigenera without general type assumption. In this talk, we will focus on the division theorem / problem and talk about its currently known cases (old and new). One motivation comes from yet another viewpoint on the finite generation of canonical ring.

#### Seminar on Geometric Complex Analysis

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

Asymptotics of the Bergman function for semipositive holomorphic line bundles (JAPANESE)

**Toshihiro Nose**(Kyushu Univ.)Asymptotics of the Bergman function for semipositive holomorphic line bundles (JAPANESE)

[ Abstract ]

In this talk, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kahler manifolds, whose Hermitian metric has some kind of quasihomogeneous properties. In the sence of pointwise asymptotics, This expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.

In this talk, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kahler manifolds, whose Hermitian metric has some kind of quasihomogeneous properties. In the sence of pointwise asymptotics, This expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.

### 2011/01/13

#### Operator Algebra Seminars

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

Global dimensions for fusion categories of type $(G,k)$ (ENGLISH)

**Robert Coquereaux**(CNRS/CPT)Global dimensions for fusion categories of type $(G,k)$ (ENGLISH)

### 2011/01/12

#### Number Theory Seminar

16:30-18:45 Room #056 (Graduate School of Math. Sci. Bldg.)

On regularized double shuffle relation for multiple zeta values (ENGLISH)

Spines with View Toward Modular Forms (ENGLISH)

**Zhonghua Li**(University of Tokyo) 16:30-17:30On regularized double shuffle relation for multiple zeta values (ENGLISH)

[ Abstract ]

Multiple zeta values(MZVs) are natural generalizations of Riemann zeta values. There are many rational relations among MZVs. It is conjectured that the regularized double shuffle relations contian all rational relations of MZVs. So other rational relations should be deduced from regularized dhouble shuffle relations. In this talk, we discuss some results on this problem. We define the gamma series accociated to elements satisfying regularized double shuffle relations and give some properties. Moreover we show that the Ohno-Zagier relations can be deduced from regularized double shuffle relations.

Multiple zeta values(MZVs) are natural generalizations of Riemann zeta values. There are many rational relations among MZVs. It is conjectured that the regularized double shuffle relations contian all rational relations of MZVs. So other rational relations should be deduced from regularized dhouble shuffle relations. In this talk, we discuss some results on this problem. We define the gamma series accociated to elements satisfying regularized double shuffle relations and give some properties. Moreover we show that the Ohno-Zagier relations can be deduced from regularized double shuffle relations.

**Dan Yasaki**(North Carolina University) 17:45-18:45Spines with View Toward Modular Forms (ENGLISH)

[ Abstract ]

The study of an arithmetic group is often aided by the fact that it acts naturally on a nice topological object. One can then use topological or geometric techniques to try to recover arithmetic data. For example, one often studies SL_2(Z) in terms of

its action on the upper half plane. In this talk, we will examine spines, which are the ``smallest" such spaces for a given arithmetic group. On overview of some known theoretical results and explicit computations will be given.

The study of an arithmetic group is often aided by the fact that it acts naturally on a nice topological object. One can then use topological or geometric techniques to try to recover arithmetic data. For example, one often studies SL_2(Z) in terms of

its action on the upper half plane. In this talk, we will examine spines, which are the ``smallest" such spaces for a given arithmetic group. On overview of some known theoretical results and explicit computations will be given.

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