## Seminar information archive

Seminar information archive ～05/20｜Today's seminar 05/21 | Future seminars 05/22～

### 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.

### 2011/01/11

#### Tuesday Seminar on Topology

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

The Chas-Sullivan conjecture for a surface of infinite genus (JAPANESE)

**Nariya Kawazumi**(The University of Tokyo)The Chas-Sullivan conjecture for a surface of infinite genus (JAPANESE)

[ Abstract ]

Let \\Sigma_{\\infty,1} be the inductive limit of compact

oriented surfaces with one boundary component. We prove the

center of the Goldman Lie algebra of the surface \\Sigma_{\\infty,1}

is spanned by the constant loop.

A similar statement for a closed oriented surface was conjectured

by Chas and Sullivan, and proved by Etingof. Our result is deduced

from a computation of the center of the Lie algebra of oriented chord

diagrams.

If time permits, the Lie bracket on the space of linear chord diagrams

will be discussed. This talk is based on a joint work with Yusuke Kuno

(Hiroshima U./JSPS).

Let \\Sigma_{\\infty,1} be the inductive limit of compact

oriented surfaces with one boundary component. We prove the

center of the Goldman Lie algebra of the surface \\Sigma_{\\infty,1}

is spanned by the constant loop.

A similar statement for a closed oriented surface was conjectured

by Chas and Sullivan, and proved by Etingof. Our result is deduced

from a computation of the center of the Lie algebra of oriented chord

diagrams.

If time permits, the Lie bracket on the space of linear chord diagrams

will be discussed. This talk is based on a joint work with Yusuke Kuno

(Hiroshima U./JSPS).

#### Operator Algebra Seminars

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

Noncommutative geometry and diffeomorphism-invariant geometries (ENGLISH)

**Raphael Ponge**(Univ. Tokyo)Noncommutative geometry and diffeomorphism-invariant geometries (ENGLISH)

#### Numerical Analysis Seminar

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

Norm estimates of inverse linear ordinary differential operator and its applications (JAPANESE)

[ Reference URL ]

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

**Takehiko Kinoshita**(RIMS)Norm estimates of inverse linear ordinary differential operator and its applications (JAPANESE)

[ Reference URL ]

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

### 2010/12/22

#### GCOE Seminars

11:00-12:00 Room #570 (Graduate School of Math. Sci. Bldg.)

Stability estimates for the anisotropic Schrodinger equations from the Dirichlet to Neumann map (ENGLISH)

**Mourad Bellassoued**(Faculté des Sciences de Bizerte)Stability estimates for the anisotropic Schrodinger equations from the Dirichlet to Neumann map (ENGLISH)

[ Abstract ]

In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in the Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the Schrödinger equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1 (this is a joint work with David Dos Santos Ferreira).

In this talk we want to obtain stability estimates for the inverse problem of determining the electric potential or the conformal factor in the Schrodinger equations in an anisotropic media with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the Schrödinger equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet to Neumann map for the Schrödinger equation measured on the boundary uniquely determines the electric potential and we prove H\\"older-type stability in determining the potential. We prove similar results for the determination of a conformal factor close to 1 (this is a joint work with David Dos Santos Ferreira).

#### Number Theory Seminar

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

Inductive construction of the p-adic zeta functions for non-commutative

p-extensions of totally real fields with exponent p (JAPANESE)

**Takashi Hara**(University of Tokyo)Inductive construction of the p-adic zeta functions for non-commutative

p-extensions of totally real fields with exponent p (JAPANESE)

[ Abstract ]

We will discuss how to construct p-adic zeta functions and verify

the main conjecture in special cases in non-commutative Iwasawa theory

for totally real number fields.

The non-commutative Iwasawa main conjecture for totally real number

fields has been verified in special cases by Kazuya Kato,

Mahesh Kakde and the speaker by `patching method of p-adic zeta functions'

introduced by David Burns and Kazuya Kato (Jurgen Ritter and Alfred Weiss

have also constructed the successful example of the main conjecture

under somewhat different formulations).

In this talk we will explain that we can prove the main conjecture

for cases where the Galois group is isomorphic

to the direct product of the ring of p-adic integer and a finite p-group

of exponent p by utilizing Burns-Kato's method and inductive arguments.

Finally we remark that in 2010 Ritter-Weiss and Kakde independently

justified the non-commutative main conjecture

for totally real number fields under general settings.

We will discuss how to construct p-adic zeta functions and verify

the main conjecture in special cases in non-commutative Iwasawa theory

for totally real number fields.

The non-commutative Iwasawa main conjecture for totally real number

fields has been verified in special cases by Kazuya Kato,

Mahesh Kakde and the speaker by `patching method of p-adic zeta functions'

introduced by David Burns and Kazuya Kato (Jurgen Ritter and Alfred Weiss

have also constructed the successful example of the main conjecture

under somewhat different formulations).

In this talk we will explain that we can prove the main conjecture

for cases where the Galois group is isomorphic

to the direct product of the ring of p-adic integer and a finite p-group

of exponent p by utilizing Burns-Kato's method and inductive arguments.

Finally we remark that in 2010 Ritter-Weiss and Kakde independently

justified the non-commutative main conjecture

for totally real number fields under general settings.

### 2010/12/21

#### Lie Groups and Representation Theory

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Some relation between the Weyl module and the crystal basis of the tensor product of fudamental representations (ENGLISH)

**Katsuyuki NAOI**(Graduate School of Mathematical Sciences, the University of Tokyo)Some relation between the Weyl module and the crystal basis of the tensor product of fudamental representations (ENGLISH)

### 2010/12/20

#### Seminar on Geometric Complex Analysis

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

Pseudoconvex domains in Hopf surfaces (JAPANESE)

**Hiroshi Yamaguchi**(Shiga Univ*)Pseudoconvex domains in Hopf surfaces (JAPANESE)

#### Algebraic Geometry Seminar

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

On the minimal model theory from a viewpoint of numerical invariants (JAPANESE)

**Yoshinori Gongyo**(Univ. of Tokyo)On the minimal model theory from a viewpoint of numerical invariants (JAPANESE)

[ Abstract ]

I will introduce the numerical Kodaira dimension for pseudo-effective divisors after N. Nakayama and explain the minimal model theory of numerical Kodaira dimension zero. I also will talk about the applications. ( partially joint work with B. Lehmann.)

I will introduce the numerical Kodaira dimension for pseudo-effective divisors after N. Nakayama and explain the minimal model theory of numerical Kodaira dimension zero. I also will talk about the applications. ( partially joint work with B. Lehmann.)

### 2010/12/16

#### Operator Algebra Seminars

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

Evolution of Quantum Dynamical Systems (ENGLISH)

**Marco Merkli**(Memorial Univ. Newfoundland)Evolution of Quantum Dynamical Systems (ENGLISH)

#### Operator Algebra Seminars

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

Fixed point theorems and derivations (ENGLISH)

**Nicolas Monod**(EPFL)Fixed point theorems and derivations (ENGLISH)

#### Lectures

13:00-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Credit Derivatives Modelling and the concept of Background Intensity I (ENGLISH)

**Sebastien Hitier**(BNP Paribas, Head of Quantitative Research, Credit Asia)Credit Derivatives Modelling and the concept of Background Intensity I (ENGLISH)

[ Abstract ]

Session 1: Introducing background intensity models

- Motivation for the concept of background intensity

- The default realisation marker

- Definition of background filtration and background intensity

- Reformulating the H hypothesis, and Kusuoka’s “remark”

- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models

- Generalised HJM formula for credit

- Definition of conditionally independent defaults

- Diversification effects: results on forward loss distribution

- Stronger conditional independence effect for spot loss

- Existence of a canonical copula

- Properties of the portfolio loss copula

Session 1: Introducing background intensity models

- Motivation for the concept of background intensity

- The default realisation marker

- Definition of background filtration and background intensity

- Reformulating the H hypothesis, and Kusuoka’s “remark”

- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models

- Generalised HJM formula for credit

- Definition of conditionally independent defaults

- Diversification effects: results on forward loss distribution

- Stronger conditional independence effect for spot loss

- Existence of a canonical copula

- Properties of the portfolio loss copula

#### Lectures

14:40-16:10 Room #123 (Graduate School of Math. Sci. Bldg.)

Credit Derivatives Modelling and the concept of Background Intensity II (ENGLISH)

**Sebastien Hitier**(BNP Paribas, Head of Quantitative Research, Credit Asia)Credit Derivatives Modelling and the concept of Background Intensity II (ENGLISH)

[ Abstract ]

Session 1: Introducing background intensity models

- Motivation for the concept of background intensity

- The default realisation marker

- Definition of background filtration and background intensity

- Reformulating the H hypothesis, and Kusuoka’s “remark”

- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models

- Generalised HJM formula for credit

- Definition of conditionally independent defaults

- Diversification effects: results on forward loss distribution

- Stronger conditional independence effect for spot loss

- Existence of a canonical copula

- Properties of the portfolio loss copula

Session 1: Introducing background intensity models

- Motivation for the concept of background intensity

- The default realisation marker

- Definition of background filtration and background intensity

- Reformulating the H hypothesis, and Kusuoka’s “remark”

- Generalised HJM formula and Credit Risk neutral dynamics

Session 2: Five useful properties of background intensity models

- Generalised HJM formula for credit

- Definition of conditionally independent defaults

- Diversification effects: results on forward loss distribution

- Stronger conditional independence effect for spot loss

- Existence of a canonical copula

- Properties of the portfolio loss copula

### 2010/12/14

#### Tuesday Seminar on Topology

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

On the coarse geometry of Teichmueller space (ENGLISH)

**Kenneth Schackleton**(IPMU)On the coarse geometry of Teichmueller space (ENGLISH)

[ Abstract ]

We discuss the synthetic geometry of the pants graph in

comparison with the Weil-Petersson metric, whose geometry the

pants graph coarsely models following work of Brock’s. We also

restrict our attention to the 5-holed sphere, studying the Gromov

bordification of the pants graph and the dynamics of pseudo-Anosov

mapping classes.

We discuss the synthetic geometry of the pants graph in

comparison with the Weil-Petersson metric, whose geometry the

pants graph coarsely models following work of Brock’s. We also

restrict our attention to the 5-holed sphere, studying the Gromov

bordification of the pants graph and the dynamics of pseudo-Anosov

mapping classes.

### 2010/12/13

#### Seminar on Geometric Complex Analysis

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

An equality estimate for the second main theorem (JAPANESE)

**Katsutoshi Yamanoi**(Tokyo Institute of Technology)An equality estimate for the second main theorem (JAPANESE)

#### Algebraic Geometry Seminar

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

Enumeration of plane curves and labeled floor diagrams (ENGLISH)

**Sergey Fomin**(University of Michigan)Enumeration of plane curves and labeled floor diagrams (ENGLISH)

[ Abstract ]

Floor diagrams are a class of weighted oriented graphs introduced by E. Brugalle and G. Mikhalkin. Tropical geometry arguments yield combinatorial descriptions of (ordinary and relative) Gromov-Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In the case of the projective plane, these descriptions can be used to obtain new formulas for the corresponding enumerative invariants. In particular, we give a proof of Goettsche's polynomiality conjecture for plane curves, and enumerate plane rational curves of given degree passing through given points and having maximal tangency to a given line. On the combinatorial side, we show that labeled floor diagrams of genus 0 are equinumerous to labeled trees, and therefore counted by the celebrated Cayley's formula. The corresponding bijections lead to interpretations of the Kontsevich numbers (the genus-0 Gromov-Witten invariants of the projective plane) in terms of certain statistics on trees.

This is joint work with Grisha Mikhalkin.

Floor diagrams are a class of weighted oriented graphs introduced by E. Brugalle and G. Mikhalkin. Tropical geometry arguments yield combinatorial descriptions of (ordinary and relative) Gromov-Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In the case of the projective plane, these descriptions can be used to obtain new formulas for the corresponding enumerative invariants. In particular, we give a proof of Goettsche's polynomiality conjecture for plane curves, and enumerate plane rational curves of given degree passing through given points and having maximal tangency to a given line. On the combinatorial side, we show that labeled floor diagrams of genus 0 are equinumerous to labeled trees, and therefore counted by the celebrated Cayley's formula. The corresponding bijections lead to interpretations of the Kontsevich numbers (the genus-0 Gromov-Witten invariants of the projective plane) in terms of certain statistics on trees.

This is joint work with Grisha Mikhalkin.

### 2010/12/10

#### Colloquium

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

Hamilton-Jacobi equations and crystal growth (JAPANESE)

**Yoshikazu Giga**(The University of Tokyo, Graduate School of Mathematical Sciences)Hamilton-Jacobi equations and crystal growth (JAPANESE)

### 2010/12/09

#### Operator Algebra Seminars

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

Spectral flow associated to KMS states with periodic KMS group action (ENGLISH)

**Ryszard Nest**(Univ. Copenhagen)Spectral flow associated to KMS states with periodic KMS group action (ENGLISH)

### 2010/12/07

#### Tuesday Seminar on Topology

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

Diffeomorphism-invariant geometries and noncommutative geometry (ENGLISH)

**Raphael Ponge**(The University of Tokyo)Diffeomorphism-invariant geometries and noncommutative geometry (ENGLISH)

[ Abstract ]

In many geometric situations we may encounter the action of

a group $G$ on a manifold $M$, e.g., in the context of foliations. If

the action is free and proper, then the quotient $M/G$ is a smooth

manifold. However, in general the quotient $M/G$ need not even be

Hausdorff. Furthermore, it is well-known that a manifold has structure

invariant under the full group of diffeomorphisms except the

differentiable structure itself. Under these conditions how can one do

diffeomorphism-invariant geometry?

Noncommutative geometry provides us with the solution of trading the

ill-behaved space $M/G$ for a non-commutative algebra which

essentially plays the role of the algebra of smooth functions on that

space. The local index formula of Atiyah-Singer ultimately holds in

the setting of noncommutative geometry. Using this framework Connes

and Moscovici then obtained in the 90s a striking reformulation of the

local index formula in diffeomorphism-invariant geometry.

An important part the talk will be devoted to reviewing noncommutative

geometry and Connes-Moscovici's index formula. We will then hint to on-

going projects about reformulating the local index formula in two new

geometric settings: biholomorphism-invariant geometry of strictly

pseudo-convex domains and contactomorphism-invariant geometry.

In many geometric situations we may encounter the action of

a group $G$ on a manifold $M$, e.g., in the context of foliations. If

the action is free and proper, then the quotient $M/G$ is a smooth

manifold. However, in general the quotient $M/G$ need not even be

Hausdorff. Furthermore, it is well-known that a manifold has structure

invariant under the full group of diffeomorphisms except the

differentiable structure itself. Under these conditions how can one do

diffeomorphism-invariant geometry?

Noncommutative geometry provides us with the solution of trading the

ill-behaved space $M/G$ for a non-commutative algebra which

essentially plays the role of the algebra of smooth functions on that

space. The local index formula of Atiyah-Singer ultimately holds in

the setting of noncommutative geometry. Using this framework Connes

and Moscovici then obtained in the 90s a striking reformulation of the

local index formula in diffeomorphism-invariant geometry.

An important part the talk will be devoted to reviewing noncommutative

geometry and Connes-Moscovici's index formula. We will then hint to on-

going projects about reformulating the local index formula in two new

geometric settings: biholomorphism-invariant geometry of strictly

pseudo-convex domains and contactomorphism-invariant geometry.

#### Numerical Analysis Seminar

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

Numerical verification of existence for solutions to Dirichlet

boundary value problems of semilinear elliptic equations

(JAPANESE)

[ Reference URL ]

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

**Akitoshi Takayasu**(Waseda University)Numerical verification of existence for solutions to Dirichlet

boundary value problems of semilinear elliptic equations

(JAPANESE)

[ Reference URL ]

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

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