## Seminar information archive

Seminar information archive ～12/09｜Today's seminar 12/10 | Future seminars 12/11～

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

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

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

#### Monthly Seminar on Arithmetic of Automorphic Forms

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/01/31

#### Colloquium

16:30-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Controllability of fluid flows (ENGLISH)

**Jean-Pierre Puel**(Université de Versailles Saint-Quentin-en-Yvelines)Controllability of fluid flows (ENGLISH)

[ Abstract ]

First of all we will describe in an abstract situation the various concepts

of controllability for evolution equations.

We will then present some problems and results concerning the

controllability of systems modeling fluid flows.

First of all we will consider the Euler equation describing the motion of an

incompressible inviscid fluid.

Then we will give some results concerning the Navier-Stokes equations,

modeling an incompressible viscous fluid, and some related systems.

Finally we will give a first result of controllability for the case of a

compressible fluid (in dimension 1) and some important open problems.

First of all we will describe in an abstract situation the various concepts

of controllability for evolution equations.

We will then present some problems and results concerning the

controllability of systems modeling fluid flows.

First of all we will consider the Euler equation describing the motion of an

incompressible inviscid fluid.

Then we will give some results concerning the Navier-Stokes equations,

modeling an incompressible viscous fluid, and some related systems.

Finally we will give a first result of controllability for the case of a

compressible fluid (in dimension 1) and some important open problems.

### 2014/01/30

#### Kavli IPMU Komaba Seminar

17:00-18:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Characteristic classes from 2d renormalized sigma-models (ENGLISH)

**Hans Jockers**(The University of Bonn)Characteristic classes from 2d renormalized sigma-models (ENGLISH)

[ Abstract ]

The Hirzebruch-Riemann-Roch formula relates the holomorphic Euler characteristic

of holomorphic vector bundles to topological invariants of compact complex manifold.

I will explain a generalization of the Mukai's modified first Chern character map, which

introduces certain characteristic classes that have not been considered in this form by

Hirzebruch. This naturally leads to the characteristic Gamma class based on the Gamma

function. The characteristic Gamma class has a surprising relation to the quantum theory

of certain 2d sigma-models with compact complex manifolds as their target spaces. I will

argue that the Gamma class describes perturbative quantum corrections to the classical

theory of those sigma models.

The Hirzebruch-Riemann-Roch formula relates the holomorphic Euler characteristic

of holomorphic vector bundles to topological invariants of compact complex manifold.

I will explain a generalization of the Mukai's modified first Chern character map, which

introduces certain characteristic classes that have not been considered in this form by

Hirzebruch. This naturally leads to the characteristic Gamma class based on the Gamma

function. The characteristic Gamma class has a surprising relation to the quantum theory

of certain 2d sigma-models with compact complex manifolds as their target spaces. I will

argue that the Gamma class describes perturbative quantum corrections to the classical

theory of those sigma models.

### 2014/01/28

#### Numerical Analysis Seminar

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

Mathematical models of cell-cell adhesion (JAPANESE)

[ Reference URL ]

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

**Hideki Murakawa**(Kyushu University)Mathematical models of cell-cell adhesion (JAPANESE)

[ Reference URL ]

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

#### Tuesday Seminar of Analysis

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

Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

**Arnaud Ducrot**(University of Bordeaux)Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

[ Abstract ]

In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

#### GCOE Seminars

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

Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

http://agusta.ms.u-tokyo.ac.jp/analysis.html

**Arnaud Ducrot**(University of Bordeaux)Asymptotic behaviour of a non-local diffusive logistic equation (ENGLISH)

[ Abstract ]

In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

[ Reference URL ]In this talk we investigate the long time behaviour of a logistic type equation modelling the motion of cells. The equation we consider takes into account birth and death process using a simple logistic effect as well as a non-local motion of cells using non-local Darcy’s law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behaviour. The lack of asymptotic compactness of the system is overcome by making use of Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

http://agusta.ms.u-tokyo.ac.jp/analysis.html

### 2014/01/27

#### Seminar on Geometric Complex Analysis

11:00-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Logarithmic 1-forms and distributions of entire curves and integral points (JAPANESE)

**Junjiro Noguchi**(The University of Tokyo)Logarithmic 1-forms and distributions of entire curves and integral points (JAPANESE)

[ Abstract ]

The Log-Bloch-Ochiai Theorem says, in the most general form so far, that every entire curve in a Zariski open $X$ of a compact Kahler manifold $\bar{X}$ must be degenerate, if $\bar{q}(X)> \dim X$ ([NW02] Noguchi-Winkelmann, Math.\ Z. 239, 2002). If $X$ is defined a quasi-projective algebraic variety defined over a number field, then there is no Zariski dense $(S, D)$-integral subset in $X$ ($D=\partial X=\bar{X}\subset X$). We discuss this kind of properties more.

In the talk we will fix an error in an application in [NW02], and we will show

Theorem 1. (i) Let $M$ be a complex projective algebraic manifold, and let $D=\sum_{j=1}^l D_j$ be a sum of divisors on $M$ which are independent in supports. If $l> \dim M+r(\{D_j\})-q(M)$, then every entire curve $f:\mathbf{C} \to M\setminus D$ must be degenerate.

(ii) Let $M$ and $D_j$ be defined over a number field. If $l> \dim M+r(\{D_j\})-q(M)$, then there is no Zariski-dense $(S,D)$-integral subset of $M\setminus D$.

For the finiteness we obtain

Theorem 2. Let the notation be as above.

(i) If $l \geq 2 \dim M+r(\{D_j\})$, then $M\setminus D$ is completehyperbolic and hyperbolically embedded into $M$.

(ii) Let $M$ and $D_j$ be defined over a number field. If $l> 2\dim M+r(\{D_j\})$, then every $(S,D)$-integral subset of $M\setminus D$ is finite.

Precise definitions will be given in the talk. We will also discuss an application of Theorem 1 (ii) to generalize Siegel's Theorem on integral points on affine curves,

recent due to A. Levin.

The Log-Bloch-Ochiai Theorem says, in the most general form so far, that every entire curve in a Zariski open $X$ of a compact Kahler manifold $\bar{X}$ must be degenerate, if $\bar{q}(X)> \dim X$ ([NW02] Noguchi-Winkelmann, Math.\ Z. 239, 2002). If $X$ is defined a quasi-projective algebraic variety defined over a number field, then there is no Zariski dense $(S, D)$-integral subset in $X$ ($D=\partial X=\bar{X}\subset X$). We discuss this kind of properties more.

In the talk we will fix an error in an application in [NW02], and we will show

Theorem 1. (i) Let $M$ be a complex projective algebraic manifold, and let $D=\sum_{j=1}^l D_j$ be a sum of divisors on $M$ which are independent in supports. If $l> \dim M+r(\{D_j\})-q(M)$, then every entire curve $f:\mathbf{C} \to M\setminus D$ must be degenerate.

(ii) Let $M$ and $D_j$ be defined over a number field. If $l> \dim M+r(\{D_j\})-q(M)$, then there is no Zariski-dense $(S,D)$-integral subset of $M\setminus D$.

For the finiteness we obtain

Theorem 2. Let the notation be as above.

(i) If $l \geq 2 \dim M+r(\{D_j\})$, then $M\setminus D$ is completehyperbolic and hyperbolically embedded into $M$.

(ii) Let $M$ and $D_j$ be defined over a number field. If $l> 2\dim M+r(\{D_j\})$, then every $(S,D)$-integral subset of $M\setminus D$ is finite.

Precise definitions will be given in the talk. We will also discuss an application of Theorem 1 (ii) to generalize Siegel's Theorem on integral points on affine curves,

recent due to A. Levin.

### 2014/01/25

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)

Analysis of mass-subcritical nonlinear Schrödinger equation (JAPANESE)

**Jayson Cunanan**(Nagoya University) 13:30-15:00Unimodular Fourier multipliers on Wiener Amalgam Spaces (JAPANESE)

**Satoshi Masaki**(Hiroshima University) 15:30-17:00Analysis of mass-subcritical nonlinear Schrödinger equation (JAPANESE)

### 2014/01/24

#### Number Theory Seminar

16:40-18:50 Room #056 (Graduate School of Math. Sci. Bldg.)

An approach to p-adic Hodge theory over number fields (ENGLISH)

Canonical lifts of norm fields and applications (ENGLISH)

**Christopher Davis**(University of Copenhagen) 16:40-17:40An approach to p-adic Hodge theory over number fields (ENGLISH)

[ Abstract ]

As motivation from classical Hodge theory, we will first compare singular cohomology and (algebraic) de Rham cohomology for a complex analytic variety. We will also describe a sense in which this comparison does not have a natural analogue over the real numbers. We think of the complex numbers as a "big" ring which is necessary for the comparison isomorphism to work. In the p-adic setting, the analogous study is known as p-adic Hodge theory, and the "big" rings there are even bigger. There are many approaches to p-adic Hodge theory, and we will introduce one tool in particular: (phi, Gamma)-modules. The goal of this talk is to describe a preliminary attempt to find an analogue of this theory (and analogues of its "big" rings) which makes sense over number fields (rather than p-adic fields). This is joint work with Kiran Kedlaya.

As motivation from classical Hodge theory, we will first compare singular cohomology and (algebraic) de Rham cohomology for a complex analytic variety. We will also describe a sense in which this comparison does not have a natural analogue over the real numbers. We think of the complex numbers as a "big" ring which is necessary for the comparison isomorphism to work. In the p-adic setting, the analogous study is known as p-adic Hodge theory, and the "big" rings there are even bigger. There are many approaches to p-adic Hodge theory, and we will introduce one tool in particular: (phi, Gamma)-modules. The goal of this talk is to describe a preliminary attempt to find an analogue of this theory (and analogues of its "big" rings) which makes sense over number fields (rather than p-adic fields). This is joint work with Kiran Kedlaya.

**Bryden Cais**(University of Arizona) 17:50-18:50Canonical lifts of norm fields and applications (ENGLISH)

[ Abstract ]

In this talk, we begin by outlining the Fontaine-Wintenberger theory of norm fields and explain its application to the classification of p-adic Galois representations on F_p-vector spaces. In order to lift this to a classification of p-adic representations on Z_p-modules, it is necessary to lift the characteristic p norm field constructions of Fontaine-Wintenberger to characteristic zero. We will explain how to canonically perform such lifting in many interesting cases, as well as applications to generalizing a theorem of Kisin on the restriction of crystalline p-adic Galois representations. This is joint work with Christopher Davis.

In this talk, we begin by outlining the Fontaine-Wintenberger theory of norm fields and explain its application to the classification of p-adic Galois representations on F_p-vector spaces. In order to lift this to a classification of p-adic representations on Z_p-modules, it is necessary to lift the characteristic p norm field constructions of Fontaine-Wintenberger to characteristic zero. We will explain how to canonically perform such lifting in many interesting cases, as well as applications to generalizing a theorem of Kisin on the restriction of crystalline p-adic Galois representations. This is joint work with Christopher Davis.

#### Colloquium

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

Complex Brunn-Minkowski theory (ENGLISH)

**Bo Berndtsson**(Chalmers University of Technology)Complex Brunn-Minkowski theory (ENGLISH)

[ Abstract ]

The classical Brunn-Minkowski theory deals with the volume of convex sets.

It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.

The classical Brunn-Minkowski theory deals with the volume of convex sets.

It can be formulated as a statement about how the volume of slices of a convex set varies when the slice changes. Its complex counterpart deals with slices of pseudo convex sets, or more generally fibers of a complex fibration. It describes how $L^2$-norms of holomorphic functions, or sections of a line bundle, vary when the fibers change, and says essentially that a certain associated vector bundle has positive curvature. In the presence of enough symmetry this implies convexity properties of volumes; the real Brunn-Minkowski theorem corresponding to maximal symmetry. There are also applications and relations in other directions, like variations of Kahler metrics, variations of complex structures and the study of plurisubharmonic functions.

### 2014/01/23

#### Applied Analysis

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

Inside dynamics of pushed and pulled fronts (ENGLISH)

**Thomas Giletti**(Univ. of Lorraine at Nancy)Inside dynamics of pushed and pulled fronts (ENGLISH)

[ Abstract ]

Mathematical analysis of reaction-diffusion equations is a powerful tool in the understanding of dynamics of many real-life propagation phenomena. A feature of particular interest is the fact that dynamics and their underlying mechanisms vary greatly, depending on the choice of the nonlinearity in the reaction term. In this talk, we will discuss the pushed/pulled front terminology, based upon the role of each component of the front inside the whole propagating structure.

Mathematical analysis of reaction-diffusion equations is a powerful tool in the understanding of dynamics of many real-life propagation phenomena. A feature of particular interest is the fact that dynamics and their underlying mechanisms vary greatly, depending on the choice of the nonlinearity in the reaction term. In this talk, we will discuss the pushed/pulled front terminology, based upon the role of each component of the front inside the whole propagating structure.

### 2014/01/22

#### Number Theory Seminar

18:00-19:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Riemann-Hilbert correspondence for irregular holonomic D-modules (ENGLISH)

**Masaki Kashiwara**(RIMS, Kyoto University)Riemann-Hilbert correspondence for irregular holonomic D-modules (ENGLISH)

[ Abstract ]

The classical Riemann-Hilbert correspondence establishes an equivalence between the derived category of regular holonomic D-modules and the derived category of constructible sheaves. Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves on the product of the base space and the real projective line. The construction is therefore based on the theory of ind-sheaves by Kashiwara-Schapira, and also it is influenced by Tamarkin's work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Takuro Mochizuki and Kiran Kedlaya.

The classical Riemann-Hilbert correspondence establishes an equivalence between the derived category of regular holonomic D-modules and the derived category of constructible sheaves. Recently, I, with Andrea D'Agnolo, proved a Riemann-Hilbert correspondence for holonomic D-modules which are not necessarily regular (arXiv:1311.2374). In this correspondence, we have to replace the derived category of constructible sheaves with a full subcategory of ind-sheaves on the product of the base space and the real projective line. The construction is therefore based on the theory of ind-sheaves by Kashiwara-Schapira, and also it is influenced by Tamarkin's work. Among the main ingredients of our proof is the description of the structure of flat meromorphic connections due to Takuro Mochizuki and Kiran Kedlaya.

#### Algebraic Geometry Seminar

15:00-16:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Divisorial Extractions from Singular Curves in Smooth 3-Folds (ENGLISH)

**Thomas Ducat**(University of Warwick)Divisorial Extractions from Singular Curves in Smooth 3-Folds (ENGLISH)

[ Abstract ]

Consider a singular curve C contained in a smooth 3-fold X.

Assuming the existence of a Du Val general elephant S containing C,

I give a normal form for the equations of C in X and an outline of how to

construct a divisorial extraction from this curve. If the general S is

Du Val of type D_{2k}, E_6 or E_7 then I can give some explicit

conditions for the existence of a terminal extraction. A treatment of

the D_{2k+1} case should be possible by similar means.

Consider a singular curve C contained in a smooth 3-fold X.

Assuming the existence of a Du Val general elephant S containing C,

I give a normal form for the equations of C in X and an outline of how to

construct a divisorial extraction from this curve. If the general S is

Du Val of type D_{2k}, E_6 or E_7 then I can give some explicit

conditions for the existence of a terminal extraction. A treatment of

the D_{2k+1} case should be possible by similar means.

### 2014/01/21

#### Tuesday Seminar of Analysis

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

An improved level set method based on comparison with a signed distance function (JAPANESE)

**Nao Hamamuki**(Graduate shool of Mathematical Sciences, the University of Tokyo)An improved level set method based on comparison with a signed distance function (JAPANESE)

[ Abstract ]

In the classical level set method, a slope of a solution to level set

equations can be close to zero as time develops even if the initial

slope is large, and this prevents one from computing interfaces given as

the level set of the solution. To overcome this issue we introduce an

improved equation by adding an extra term to the original equation.

Then, by applying a comparison principle to the signed distance function

to the interface, we prove that, globally in time, the slope of a

solution of the initial value problem is preserved near the zero level set.

In the classical level set method, a slope of a solution to level set

equations can be close to zero as time develops even if the initial

slope is large, and this prevents one from computing interfaces given as

the level set of the solution. To overcome this issue we introduce an

improved equation by adding an extra term to the original equation.

Then, by applying a comparison principle to the signed distance function

to the interface, we prove that, globally in time, the slope of a

solution of the initial value problem is preserved near the zero level set.

#### Tuesday Seminar on Topology

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

On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)

**Naohiko Kasuya**(The University of Tokyo)On contact submanifolds of the odd dimensional Euclidean space (JAPANESE)

[ Abstract ]

We prove that the Chern class of a closed contact manifold is an

obstruction for codimension two contact embeddings in the odd

dimensional Euclidean space.

By Gromov's h-principle,

for any closed contact $3$-manifold with trivial first Chern class,

there is a contact structure on $\\mathbb{R}^5$ which admits a contact

embedding.

We prove that the Chern class of a closed contact manifold is an

obstruction for codimension two contact embeddings in the odd

dimensional Euclidean space.

By Gromov's h-principle,

for any closed contact $3$-manifold with trivial first Chern class,

there is a contact structure on $\\mathbb{R}^5$ which admits a contact

embedding.

#### Tuesday Seminar on Topology

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

Weak eigenvalues in homoclinic classes: perturbations from saddles

with small angles (ENGLISH)

**Xiaolong Li**(The University of Tokyo)Weak eigenvalues in homoclinic classes: perturbations from saddles

with small angles (ENGLISH)

[ Abstract ]

For 3-dimensional homoclinic classes of saddles with index 2, a

new sufficient condition for creating weak contracting eigenvalues is

provided. Our perturbation makes use of small angles between stable and

unstable subspaces of saddles. In particular, by recovering the unstable

eigenvector, we can designate that the newly created weak eigenvalue is

contracting. As applications, we obtain C^1-generic non-trivial index-

intervals of homoclinic classes and the C^1-approximation of robust

heterodimensional cycles. In particular, this sufficient condition is

satisfied by a substantial class of saddles with homoclinic tangencies.

For 3-dimensional homoclinic classes of saddles with index 2, a

new sufficient condition for creating weak contracting eigenvalues is

provided. Our perturbation makes use of small angles between stable and

unstable subspaces of saddles. In particular, by recovering the unstable

eigenvector, we can designate that the newly created weak eigenvalue is

contracting. As applications, we obtain C^1-generic non-trivial index-

intervals of homoclinic classes and the C^1-approximation of robust

heterodimensional cycles. In particular, this sufficient condition is

satisfied by a substantial class of saddles with homoclinic tangencies.

### 2014/01/20

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

タイヒミュラー距離の幾何学とその応用 (JAPANESE)

**Hideki Miyachi**(Osaka University)タイヒミュラー距離の幾何学とその応用 (JAPANESE)

#### GCOE Seminars

16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)

Increasing stability in the inverse problems for the Helmholtz type prposed equations (ENGLISH)

**Victor Isakov**(The Wichita State University)Increasing stability in the inverse problems for the Helmholtz type prposed equations (ENGLISH)

[ Abstract ]

We report on new stability estimates for recovery of the near field from the prposed scattering amplitude prposed and for Schroedinger potential from the Dirichlet-to Neumann map. In these prposed esrtimates prposed unstable (logarithmic part) goes to zero as the wave number grows. Proofs prposed are using prposed new bounds for Hankel functions and complex and real geometrical optics prposed solutions.

We report on new stability estimates for recovery of the near field from the prposed scattering amplitude prposed and for Schroedinger potential from the Dirichlet-to Neumann map. In these prposed esrtimates prposed unstable (logarithmic part) goes to zero as the wave number grows. Proofs prposed are using prposed new bounds for Hankel functions and complex and real geometrical optics prposed solutions.

#### Algebraic Geometry Seminar

15:30-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Deforming elephants of Q-Fano 3-folds (ENGLISH)

**Taro Sano**(University of Warwick)Deforming elephants of Q-Fano 3-folds (ENGLISH)

[ Abstract ]

Shokurov and Reid proved that a Fano 3-fold with canonical

Gorenstein singularities has a Du Val elephant, that is,

a member of the anticanonical linear system with only Du Val singularities.

The classification of Fano 3-folds is based on this fact.

However, for a Fano 3-fold with non-Gorenstein terminal singularities,

the anticanonical system does not contain such a member in general.

Alt{\\i}nok--Brown--Reid conjectured that, if the anticanonical system is non-empty,

a Q-Fano 3-fold can be deformed to that with a Du Val elephant.

In this talk, I will explain how to deform an elephant with isolated

singularities to a Du Val elephant.

Shokurov and Reid proved that a Fano 3-fold with canonical

Gorenstein singularities has a Du Val elephant, that is,

a member of the anticanonical linear system with only Du Val singularities.

The classification of Fano 3-folds is based on this fact.

However, for a Fano 3-fold with non-Gorenstein terminal singularities,

the anticanonical system does not contain such a member in general.

Alt{\\i}nok--Brown--Reid conjectured that, if the anticanonical system is non-empty,

a Q-Fano 3-fold can be deformed to that with a Du Val elephant.

In this talk, I will explain how to deform an elephant with isolated

singularities to a Du Val elephant.

### 2014/01/15

#### FMSP Lectures

14:50-16:20 Room #056 (Graduate School of Math. Sci. Bldg.)

Lectures on quantum Teichmüller theory IV (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

**Rinat Kashaev**(University of Geneva)Lectures on quantum Teichmüller theory IV (ENGLISH)

[ Abstract ]

Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.

In these lectures it is planned to address the following subjects:

1) Penner’s coordinates in the decorated Teichmüller space.

2) Ratio coordinates.

3) Quantization.

4) The length spectrum of simple closed curves.

[ Reference URL ]Quantum Teichmüller theory leads to a family of unitary infinite dimensional projective representations of the mapping class groups of punctured surfaces. One of the recent applications of this theory is the construction of state integral three-manifold invariants related with hyperbolic geometry.

In these lectures it is planned to address the following subjects:

1) Penner’s coordinates in the decorated Teichmüller space.

2) Ratio coordinates.

3) Quantization.

4) The length spectrum of simple closed curves.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Kashaev.pdf

#### Operator Algebra Seminars

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

Wedge-local fields in integrable models with bound states (JAPANESE)

**Yoh Tanimoto**(Univ. Tokyo)Wedge-local fields in integrable models with bound states (JAPANESE)

#### GCOE Seminars

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

Increasing stability of the continuation for the Helmholtz type equations (ENGLISH)

**Victor Isakov**(The Wichita State University)Increasing stability of the continuation for the Helmholtz type equations (ENGLISH)

[ Abstract ]

We derive conditional stability estimates for the Helmholtz type equations which are becoming of Lipschitz type for large frequencies/wave numbers. Proofs use splitting solutions into low and high frequencies parts where we use energy (in particular) Carleman estimates. We discuss numerical confirmation and open problems.

We derive conditional stability estimates for the Helmholtz type equations which are becoming of Lipschitz type for large frequencies/wave numbers. Proofs use splitting solutions into low and high frequencies parts where we use energy (in particular) Carleman estimates. We discuss numerical confirmation and open problems.

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