## Seminar information archive

Seminar information archive ～05/25｜Today's seminar 05/26 | Future seminars 05/27～

#### Seminar on Geometric Complex Analysis

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

Twistor correspondence for R-invariant indefinite self-dual metric on R^4 (JAPANESE)

**Fuminori Nakata**(Tokyo University of Science)Twistor correspondence for R-invariant indefinite self-dual metric on R^4 (JAPANESE)

#### GCOE lecture series

13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)

TBA(中止になりました) (ENGLISH)

**Mihai Paun**(Institut Élie Cartan and KIAS)TBA(中止になりました) (ENGLISH)

### 2012/01/20

#### Kavli IPMU Komaba Seminar

14:45-16:15 Room #056 (Graduate School of Math. Sci. Bldg.)

Refined holomorphic anomaly equations (ENGLISH)

**Albrecht Klemm**(The University of Bonn)Refined holomorphic anomaly equations (ENGLISH)

[ Abstract ]

We propose a derivation of refined holomophic

anomaly equation from the word-sheet point of

view and discuss the interpretation of the

refined BPS invariants for local Calabi-Yau

spaces.

We propose a derivation of refined holomophic

anomaly equation from the word-sheet point of

view and discuss the interpretation of the

refined BPS invariants for local Calabi-Yau

spaces.

### 2012/01/19

#### Applied Analysis

16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Undercompressible shocks and moving phase boundaries

(ENGLISH)

**Philippe G. LeFloch**(Univ. Paris 6 / CNRS)Undercompressible shocks and moving phase boundaries

(ENGLISH)

[ Abstract ]

I will present a study of traveling wave solutions to third-order, diffusive-dispersive equations, which arise in the modeling of complex fluid flows and represent regularization-sensitive wave patterns, especially undercompressive shock waves and moving phase boundaries. The qualitative properties of these (possibly oscillatory) traveling waves are well-understood in terms of the so-called kinetic relation, and this has led to a new theory of (nonclassical) solutions to nonlinear hyperbolic systems. Relevant papers are available at the link: www.philippelefloch.org.

I will present a study of traveling wave solutions to third-order, diffusive-dispersive equations, which arise in the modeling of complex fluid flows and represent regularization-sensitive wave patterns, especially undercompressive shock waves and moving phase boundaries. The qualitative properties of these (possibly oscillatory) traveling waves are well-understood in terms of the so-called kinetic relation, and this has led to a new theory of (nonclassical) solutions to nonlinear hyperbolic systems. Relevant papers are available at the link: www.philippelefloch.org.

### 2012/01/18

#### GCOE lecture series

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

TBA(中止になりました) (ENGLISH)

**Mihai Paun**(Institut Élie Cartan and KIAS)TBA(中止になりました) (ENGLISH)

### 2012/01/17

#### Tuesday Seminar on Topology

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

On the Johnson cokernels of the mapping class group of a surface (joint work with Naoya Enomoto) (JAPANESE)

**Takao Satoh**(Tokyo University of Science)On the Johnson cokernels of the mapping class group of a surface (joint work with Naoya Enomoto) (JAPANESE)

[ Abstract ]

In general, the Johnson homomorphisms of the mapping class group of a surface are used to investigate graded quotients of the Johnson filtration of the mapping class group. These graded quotients are considered as a sequence of approximations of the Torelli group. Now, there is a broad range of remarkable results for the Johnson homomorphisms.

In this talk, we concentrate our focus on the cokernels of the Johnson homomorphisms of the mapping class group. By a work of Shigeyuki Morita and Hiroaki Nakamura, it is known that an Sp-irreducible module [k] appears in the cokernel of the k-th Johnson homomorphism with multiplicity one if k=2m+1 for any positive integer m. In general, however, to determine Sp-structure of the cokernel is quite a difficult preblem.

Our goal is to show that we have detected new irreducible components in the cokernels. More precisely, we will show that there appears an Sp-irreducible module [1^k] in the cokernel of the k-th Johnson homomorphism with multiplicity one if k=4m+1 for any positive integer m.

In general, the Johnson homomorphisms of the mapping class group of a surface are used to investigate graded quotients of the Johnson filtration of the mapping class group. These graded quotients are considered as a sequence of approximations of the Torelli group. Now, there is a broad range of remarkable results for the Johnson homomorphisms.

In this talk, we concentrate our focus on the cokernels of the Johnson homomorphisms of the mapping class group. By a work of Shigeyuki Morita and Hiroaki Nakamura, it is known that an Sp-irreducible module [k] appears in the cokernel of the k-th Johnson homomorphism with multiplicity one if k=2m+1 for any positive integer m. In general, however, to determine Sp-structure of the cokernel is quite a difficult preblem.

Our goal is to show that we have detected new irreducible components in the cokernels. More precisely, we will show that there appears an Sp-irreducible module [1^k] in the cokernel of the k-th Johnson homomorphism with multiplicity one if k=4m+1 for any positive integer m.

#### Numerical Analysis Seminar

17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Numerical computations of flow problems with the moving boundary by an area-preserving scheme (JAPANESE)

[ Reference URL ]

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

**Daisuke Tagami**(Kyushu University)Numerical computations of flow problems with the moving boundary by an area-preserving scheme (JAPANESE)

[ Reference URL ]

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

### 2012/01/16

#### Algebraic Geometry Seminar

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

TBA(Cancelled) (JAPANESE)

**Mihai Paun**(Institut Élie Cartan and KIAS)TBA(Cancelled) (JAPANESE)

#### Seminar on Geometric Complex Analysis

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

A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic 3-space (JAPANESE)

**Yu Kawakami**(Yamaguchi University)A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic 3-space (JAPANESE)

[ Abstract ]

We provide an effective ramification theorem for the ratio of canonical forms of weakly complete flat fronts in the hyperbolic 3-space. As an application, we give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic 3-space.

We provide an effective ramification theorem for the ratio of canonical forms of weakly complete flat fronts in the hyperbolic 3-space. As an application, we give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic 3-space.

#### Operator Algebra Seminars

16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Is an irng singly generated as an ideal? (JAPANESE)

**Narutaka Ozawa**(RIMS, Kyoto University)Is an irng singly generated as an ideal? (JAPANESE)

#### GCOE lecture series

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

TBA(中止になりました) (ENGLISH)

**Mihai Paun**(Institut Élie Cartan and KIAS)TBA(中止になりました) (ENGLISH)

### 2012/01/12

#### Number Theory Seminar

18:15-19:15 Room #056 (Graduate School of Math. Sci. Bldg.)

New perspectives on the Breuil-Mézard conjecture (joint with M. Emerton)

(ENGLISH)

**Toby Gee**(Imperial College London)New perspectives on the Breuil-Mézard conjecture (joint with M. Emerton)

(ENGLISH)

[ Abstract ]

I will discuss joint work with Matthew Emerton on geometric approaches to the Breuil-Mézard conjecture, generalising a geometric approach of Breuil and Mézard. I will discuss a proof of the geometric version of the original conjecture, as well as work in progress on a geometric version of the conjecture which does not make use of a fixed residual representation.

(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。)

I will discuss joint work with Matthew Emerton on geometric approaches to the Breuil-Mézard conjecture, generalising a geometric approach of Breuil and Mézard. I will discuss a proof of the geometric version of the original conjecture, as well as work in progress on a geometric version of the conjecture which does not make use of a fixed residual representation.

(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。)

### 2012/01/06

#### Operator Algebra Seminars

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

Diagrammatical methods in theory of subfactors (ENGLISH)

**Yasuyuki Kawahigashi**(Univ. Tokyo)Diagrammatical methods in theory of subfactors (ENGLISH)

### 2012/01/05

#### Operator Algebra Seminars

16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Classification and amenability in theory of von Neumann algebras (ENGLISH)

**Yasuyuki Kawahigashi**(Univ. Tokyo)Classification and amenability in theory of von Neumann algebras (ENGLISH)

### 2011/12/27

#### Operator Algebra Seminars

14:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Deformation of algebras associated to group cocycles (JAPANESE)

Construction of wedge-local nets through

Longo-Witten endomorphisms (JAPANESE)

**Makoto Yamashita**(Universita di Roma "Tor Vergata") 14:30-16:00Deformation of algebras associated to group cocycles (JAPANESE)

**Yoh Tanimoto**(Universitaet Goettingen) 16:30-18:00Construction of wedge-local nets through

Longo-Witten endomorphisms (JAPANESE)

#### GCOE Seminars

13:30-14:30 Room #370 (Graduate School of Math. Sci. Bldg.)

The Modelling of Dislocations in the Early Stage of the Metal Fatigue (ENGLISH)

**Yichao Zhu**(University of Oxford)The Modelling of Dislocations in the Early Stage of the Metal Fatigue (ENGLISH)

[ Abstract ]

Understanding fatigue of metal under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and the aeroplane engine. Experimentally it has been found that this type of

fatigue is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB) at a microscopic level. In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analysed by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analysed by using a method of multiple scales.

Understanding fatigue of metal under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and the aeroplane engine. Experimentally it has been found that this type of

fatigue is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB) at a microscopic level. In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analysed by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analysed by using a method of multiple scales.

#### GCOE Seminars

14:30-15:30 Room #370 (Graduate School of Math. Sci. Bldg.)

Wave Transport in Random Media and Inverse Problems (ENGLISH)

**Manabu Machida**(University of Michigan)Wave Transport in Random Media and Inverse Problems (ENGLISH)

[ Abstract ]

Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.

Wave transport in random media is described by the radiative transport equation, which is a linear Boltzmann equation. Such transport phenomena are characterized by two optical parameters in the equation: the absorption and scattering coefficients. In this talk, inverse problems of determining optical parameters will be considered and the Lipschitz stability will be proved using a Carleman estimate. One application of this inverse problem is optical tomography, which detects tumors in a human body using (unlike X-ray CT scan) near-infrared light. I will also present tomographic images of lemon and lotus root slices which are obtained by numerically solving the radiative transport equation with the method of rotated reference frames.

### 2011/12/26

#### Algebraic Geometry Seminar

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

Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces (JAPANESE)

**Takuzo Okada**(Kyoto University)Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces (JAPANESE)

[ Abstract ]

It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.

It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.

### 2011/12/21

#### Number Theory Seminar

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

On Sharifi's conjecture (JAPANESE)

**Kazuya Kato**(University of Chicago)On Sharifi's conjecture (JAPANESE)

### 2011/12/20

#### Tuesday Seminar of Analysis

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

A trace formula for the perturbed Landau Hamiltonian (ENGLISH)

**Gueorgui Raykov**(Catholic University of Chile)A trace formula for the perturbed Landau Hamiltonian (ENGLISH)

[ Abstract ]

The talk will be based on a joint work with A. Pushnitski

and C. Villegas-Blas, the preprint is available here:

http://arxiv.org/abs/1110.3098 .

The talk will be based on a joint work with A. Pushnitski

and C. Villegas-Blas, the preprint is available here:

http://arxiv.org/abs/1110.3098 .

#### Tuesday Seminar on Topology

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

Leafwise symplectic structures on Lawson's Foliation on the 5-sphere (JAPANESE)

**Yoshihiko Mitsumatsu**(Chuo University)Leafwise symplectic structures on Lawson's Foliation on the 5-sphere (JAPANESE)

[ Abstract ]

We are going to show that Lawson's foliation on the 5-sphere

admits a smooth leafwise symplectic sturcture. Historically, Lawson's

foliation is the first one among foliations of codimension one which are

constructed on the 5-sphere. It is obtained by modifying the Milnor

fibration associated with the Fermat type cubic polynominal in three

variables.

Alberto Verjovsky proposed a question whether if the Lawson's

foliation or slighty modified ones admit a leafwise smooth symplectic

structure and/or a leafwise complex structure. As Lawson's one has a

Kodaira-Thurston nil 4-manifold as a compact leaf, the question can not

be solved simultaneously both for the symplectic and the complex cases.

The main part of the construction is to show that the Fermat type

cubic surface admits an `end-periodic' symplectic structure, while the

natural one as an affine surface is conic at the end. Even though for

the other two families of the simple elliptic hypersurface singularities

almost the same construction works, at present, it seems very limited

where a Stein manifold admits an end-periodic symplectic structure. If

the time allows, we also discuss the existence of such structures on

globally convex symplectic manifolds.

We are going to show that Lawson's foliation on the 5-sphere

admits a smooth leafwise symplectic sturcture. Historically, Lawson's

foliation is the first one among foliations of codimension one which are

constructed on the 5-sphere. It is obtained by modifying the Milnor

fibration associated with the Fermat type cubic polynominal in three

variables.

Alberto Verjovsky proposed a question whether if the Lawson's

foliation or slighty modified ones admit a leafwise smooth symplectic

structure and/or a leafwise complex structure. As Lawson's one has a

Kodaira-Thurston nil 4-manifold as a compact leaf, the question can not

be solved simultaneously both for the symplectic and the complex cases.

The main part of the construction is to show that the Fermat type

cubic surface admits an `end-periodic' symplectic structure, while the

natural one as an affine surface is conic at the end. Even though for

the other two families of the simple elliptic hypersurface singularities

almost the same construction works, at present, it seems very limited

where a Stein manifold admits an end-periodic symplectic structure. If

the time allows, we also discuss the existence of such structures on

globally convex symplectic manifolds.

### 2011/12/19

#### Number Theory Seminar

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

Galois Theory: Past and Present (ENGLISH)

**Tamas Szamuely**(Budapest)Galois Theory: Past and Present (ENGLISH)

### 2011/12/17

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

On the finite order Q-rational points on J_1 (N) (JAPANESE)

) 15:00-16:00

On the affineness of distinguished Deligne-Lusztig varieties (JAPANESE)

**Masami Ohta**(Professor Emeritus of Tokai Univeristy) 13:30-14:30On the finite order Q-rational points on J_1 (N) (JAPANESE)

**Shushi Harashita**(Yokohama National University) 15:00-16:00

On the affineness of distinguished Deligne-Lusztig varieties (JAPANESE)

### 2011/12/16

#### Colloquium

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

Application of positive characteristic methods to singularity theory (JAPANESE)

**TAKAGI, Shunsuke**(Graduate School of Mathematical Sciences, University of Tokyo)Application of positive characteristic methods to singularity theory (JAPANESE)

[ Abstract ]

As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.

As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.

### 2011/12/14

#### Number Theory Seminar

17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Good and bad reduction for algebraic dynamical systems (ENGLISH)

**Lucien Szpiro**(City University of New York)Good and bad reduction for algebraic dynamical systems (ENGLISH)

[ Abstract ]

We will report on a recent work with collaborators in New York on the

different ways to look at degenerations of a dynamical system in a one

parameter family. Resultants, conductors and isotriviality will be analyzed.

We will report on a recent work with collaborators in New York on the

different ways to look at degenerations of a dynamical system in a one

parameter family. Resultants, conductors and isotriviality will be analyzed.

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