## Seminar information archive

Seminar information archive ～10/03｜Today's seminar 10/04 | Future seminars 10/05～

### 2014/11/22

#### Harmonic Analysis Komaba Seminar

13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the Inclusion of Generalized Morrey Spaces and the Boundedness of the Generalized Fractional Maximal Operators (ENGLISH)

Hardy-type inequality for 0 < p < 1 and hypodecreasing functions (ENGLISH)

Sharp spectral stability estimate for uniformly elliptic differential operators (EMGLISH)

**Denny Hakim**(Tokyo Metropolitan University) 13:30-14:30On the Inclusion of Generalized Morrey Spaces and the Boundedness of the Generalized Fractional Maximal Operators (ENGLISH)

[ Abstract ]

In this talk, we shall prove a necessary and sufficient condition for an inclusion property of generalized Morrey spaces. We use this property in our proof of the boundedness of the generalized fractional maximal operators on these spaces. Our result also cover the generalized weak Morrey spaces.

This research is a joint work with Y. Sawano, H. Gunawan, K.M. Limanta and A.A. Masta.

In this talk, we shall prove a necessary and sufficient condition for an inclusion property of generalized Morrey spaces. We use this property in our proof of the boundedness of the generalized fractional maximal operators on these spaces. Our result also cover the generalized weak Morrey spaces.

This research is a joint work with Y. Sawano, H. Gunawan, K.M. Limanta and A.A. Masta.

**Tamara Tararykova**(Cardiff University / Eurasian National University) 14:45-15:45Hardy-type inequality for 0 < p < 1 and hypodecreasing functions (ENGLISH)

[ Abstract ]

T.B.A.

T.B.A.

**Victor Burenkov**(Cardift School of Mathematics / Peoples' Friendship University of Russia / Steklov Institute of Mathematics) 16:00-17:00Sharp spectral stability estimate for uniformly elliptic differential operators (EMGLISH)

[ Abstract ]

T.B.A.

T.B.A.

### 2014/11/21

#### Operator Algebra Seminars

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

Introduction to Haagerup's bicentralizer paper (English)

**Reiji Tomatsu**(Hokkaido University)Introduction to Haagerup's bicentralizer paper (English)

### 2014/11/20

#### Operator Algebra Seminars

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

Introduction to Haagerup's bicentralizer paper (English)

**Reiji Tomatsu**(Hokkaido University)Introduction to Haagerup's bicentralizer paper (English)

#### Infinite Analysis Seminar Tokyo

15:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

An explicit formula for the specialization of nonsymmetric

Macdonald polynomials at $t = \infty$ (JAPANESE)

divisor function and strict partition (JAPANESE)

**Fumihiko Nomoto**(Department of Mathematics, Tokyo Institute of Technology, Graduate school of science and Engineering) 15:00-16:30An explicit formula for the specialization of nonsymmetric

Macdonald polynomials at $t = \infty$ (JAPANESE)

[ Abstract ]

Orr-Shimozono obtained an explicit formula for nonsymmetric Macdonald polynomials with Hecke parameter $t$ set to $\infty$, which is described in terms of an affine root system

and an affine Weyl group. On the basis of this work, we give another explicit formula for the specialization above, which is described in terms of the quantum Bruhat graph associated with a finite root system and a finite Weyl group.

More precisely, we interpret the specialization above as the graded character of an explicitly specified set of quantum Lakshmibai-Seshadri (LS) paths. Here we note that the set of quantum LS paths (of a given shape) provides an explicit realization of the crystal basis of a quantum Weyl module over the quantum affine algebra.

In this talk, I will explain our explicit formula

by exhibiting a few examples.

Also, I will give an outline of the proof.

Orr-Shimozono obtained an explicit formula for nonsymmetric Macdonald polynomials with Hecke parameter $t$ set to $\infty$, which is described in terms of an affine root system

and an affine Weyl group. On the basis of this work, we give another explicit formula for the specialization above, which is described in terms of the quantum Bruhat graph associated with a finite root system and a finite Weyl group.

More precisely, we interpret the specialization above as the graded character of an explicitly specified set of quantum Lakshmibai-Seshadri (LS) paths. Here we note that the set of quantum LS paths (of a given shape) provides an explicit realization of the crystal basis of a quantum Weyl module over the quantum affine algebra.

In this talk, I will explain our explicit formula

by exhibiting a few examples.

Also, I will give an outline of the proof.

**Masanori Ando**(Wakkanai Hokusei Gakuen University) 17:00-18:30divisor function and strict partition (JAPANESE)

[ Abstract ]

We know that the q-series identity of Uchimura-type is related with the divisor function.

It is obtained also as a specialization of basic hypergeometric series.

In this seminar, we interprete this identity from the point of view of combinatorics of partitions of integers.

We give its proof by using the mock involution map.

We know that the q-series identity of Uchimura-type is related with the divisor function.

It is obtained also as a specialization of basic hypergeometric series.

In this seminar, we interprete this identity from the point of view of combinatorics of partitions of integers.

We give its proof by using the mock involution map.

### 2014/11/19

#### Operator Algebra Seminars

13:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Haagerup's bicentralizer paper (English)

**Reiji Tomatsu**(Hokkaido University)Introduction to Haagerup's bicentralizer paper (English)

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

Bad reduction of curves with CM jacobians (English)

**Fabien Pazuki**(Univ Bordeaux and Univ Copenhagen)Bad reduction of curves with CM jacobians (English)

[ Abstract ]

An abelian variety defined over a number field and having complex multiplication (CM) has potentially good reduction everywhere. If a curve of positive genus which is defined over a number field has good reduction at a given finite place, then so does its jacobian variety. However, the converse statement is false already in the genus 2 case, as can be seen in the entry $[I_0-I_0-m]$ in Namikawa and Ueno's classification table of fibres in pencils of curves of genus 2. In this joint work with Philipp Habegger, our main result states that this phenomenon prevails for certain families of curves.

We prove the following result: Let F be a real quadratic number field. Up to isomorphisms there are only finitely many curves C of genus 2 defined over $\overline{\mathbb{Q}}$ with good reduction everywhere and such that the jacobian Jac(C) has CM by the maximal order of a quartic, cyclic, totally imaginary number field containing F. Hence such a curve will almost always have stable bad reduction at some prime whereas its jacobian has good reduction everywhere. A remark is that one can exhibit an infinite family of genus 2 curves with CM jacobian such that the endomorphism ring is the ring of algebraic integers in a cyclic extension of $\mathbb{Q}$ of degree 4 that contains $\mathbb{Q}(\sqrt{5})$, for example.

An abelian variety defined over a number field and having complex multiplication (CM) has potentially good reduction everywhere. If a curve of positive genus which is defined over a number field has good reduction at a given finite place, then so does its jacobian variety. However, the converse statement is false already in the genus 2 case, as can be seen in the entry $[I_0-I_0-m]$ in Namikawa and Ueno's classification table of fibres in pencils of curves of genus 2. In this joint work with Philipp Habegger, our main result states that this phenomenon prevails for certain families of curves.

We prove the following result: Let F be a real quadratic number field. Up to isomorphisms there are only finitely many curves C of genus 2 defined over $\overline{\mathbb{Q}}$ with good reduction everywhere and such that the jacobian Jac(C) has CM by the maximal order of a quartic, cyclic, totally imaginary number field containing F. Hence such a curve will almost always have stable bad reduction at some prime whereas its jacobian has good reduction everywhere. A remark is that one can exhibit an infinite family of genus 2 curves with CM jacobian such that the endomorphism ring is the ring of algebraic integers in a cyclic extension of $\mathbb{Q}$ of degree 4 that contains $\mathbb{Q}(\sqrt{5})$, for example.

#### Mathematical Biology Seminar

14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

Introduction of Adaptive Dynamics and its application to finite population (JAPANESE)

http://joefs.mind.meiji.ac.jp/~joe/

**Joe Yuichiro Wakano**(Department of Mathematical Sciences Based on Modeling and Analysis)Introduction of Adaptive Dynamics and its application to finite population (JAPANESE)

[ Abstract ]

本講演では、まず無限集団を仮定する通常のAdaptive Dynamicsを紹介し、

進化的安定性と収束安定性を解説する。また、対応する個体ベースシミュレーションを

紹介する。個体数が有限の場合に不可避的に現れる揺らぎ（遺伝的浮動）が、

進化動態に大きな影響を与えることを、まずはシミュレーション研究から示す。

揺らぎの影響を解析的に示すために、無限集団のAdaptive Dynamicsを

Replicator-Mutator方程式系（積分微分方程式系）によって定式化し、

そこから得られるモーメントの時間発展方程式（ODE）に揺らぎの項を

加えた確率微分方程式(SDE)モデルを導出し、個体数が進化的分岐に与える影響を

解析的に導出する。

[ Reference URL ]本講演では、まず無限集団を仮定する通常のAdaptive Dynamicsを紹介し、

進化的安定性と収束安定性を解説する。また、対応する個体ベースシミュレーションを

紹介する。個体数が有限の場合に不可避的に現れる揺らぎ（遺伝的浮動）が、

進化動態に大きな影響を与えることを、まずはシミュレーション研究から示す。

揺らぎの影響を解析的に示すために、無限集団のAdaptive Dynamicsを

Replicator-Mutator方程式系（積分微分方程式系）によって定式化し、

そこから得られるモーメントの時間発展方程式（ODE）に揺らぎの項を

加えた確率微分方程式(SDE)モデルを導出し、個体数が進化的分岐に与える影響を

解析的に導出する。

http://joefs.mind.meiji.ac.jp/~joe/

### 2014/11/18

#### Tuesday Seminar on Topology

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

A Modular Operad of Embedded Curves (ENGLISH)

**Charles Siegel**(Kavli IPMU)A Modular Operad of Embedded Curves (ENGLISH)

[ Abstract ]

Modular operads were introduced by Getzler and Kapranov to formalize the structure of gluing maps between moduli of stable marked curves. We present a construction of analogous gluing maps between moduli of pluri-log-canonically embedded marked curves, which fit together to give a modular operad of embedded curves. This is joint work with Satoshi Kondo and Jesse Wolfson.

Modular operads were introduced by Getzler and Kapranov to formalize the structure of gluing maps between moduli of stable marked curves. We present a construction of analogous gluing maps between moduli of pluri-log-canonically embedded marked curves, which fit together to give a modular operad of embedded curves. This is joint work with Satoshi Kondo and Jesse Wolfson.

#### Operator Algebra Seminars

13:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Haagerup's bicentralizer paper (ENGLISH)

**Reiji Tomatsu**(Hokkaido University)Introduction to Haagerup's bicentralizer paper (ENGLISH)

### 2014/11/17

#### Seminar on Geometric Complex Analysis

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

On strong K-stability of polarized algebraic manifolds (JAPANESE)

**Yasufumi Nitta**(Tokyo Institute of Technology)On strong K-stability of polarized algebraic manifolds (JAPANESE)

#### Operator Algebra Seminars

13:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to Haagerup's bicentralizer paper (English)

**Reiji Tomatsu**(Hokkaido University)Introduction to Haagerup's bicentralizer paper (English)

### 2014/11/14

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Symplectic displacement energy for exact Lagrangian immersions

(JAPANESE)

**Manabu Akaho**(Tokyo Metropolitan University)Symplectic displacement energy for exact Lagrangian immersions

(JAPANESE)

[ Abstract ]

We give an inequality of the displacement energy for exact Lagrangian immersions and the symplectic area of punctured holomorphic discs. Our approach is based on Floer homology for Lagrangian immersions and Chekanov's homotopy technique of continuations. Moreover, we discuss our inequality and the Hofer--Zehnder capacity.

We give an inequality of the displacement energy for exact Lagrangian immersions and the symplectic area of punctured holomorphic discs. Our approach is based on Floer homology for Lagrangian immersions and Chekanov's homotopy technique of continuations. Moreover, we discuss our inequality and the Hofer--Zehnder capacity.

### 2014/11/12

#### Number Theory Seminar

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

Relative (φ, Γ)-modules (English)

**Ruochuan Liu**(BICMR)Relative (φ, Γ)-modules (English)

[ Abstract ]

In this talk, we will introduce the theory of (φ, Γ)-modules for general adic spaces. This is a joint work with Kedlaya.

In this talk, we will introduce the theory of (φ, Γ)-modules for general adic spaces. This is a joint work with Kedlaya.

### 2014/11/11

#### Tuesday Seminar on Topology

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

Unifying unexpected exceptional Dehn surgeries (ENGLISH)

**Kenneth Baker**(University of Miami)Unifying unexpected exceptional Dehn surgeries (ENGLISH)

[ Abstract ]

This past summer Dunfield-Hoffman-Licata produced examples of asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space Dehn fillings through a search of the extended SnapPea census.

Examinations of these examples with Hoffman and Licata lead us to coincidences with other work in progress that gives a simple holistic topological approach towards producing and extending many of these families. In this talk we'll explicitly describe our construction and discuss related applications of the technique.

This past summer Dunfield-Hoffman-Licata produced examples of asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space Dehn fillings through a search of the extended SnapPea census.

Examinations of these examples with Hoffman and Licata lead us to coincidences with other work in progress that gives a simple holistic topological approach towards producing and extending many of these families. In this talk we'll explicitly describe our construction and discuss related applications of the technique.

#### Seminar on Probability and Statistics

16:30-17:40 Room #052 (Graduate School of Math. Sci. Bldg.)

Local Ordinal Embedding

**Terada, Yoshikazu**(CiNet / Center for Information and Neural Networks)Local Ordinal Embedding

### 2014/11/10

#### FMSP Lectures

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

Discrete Painlevé equations with periodic coefficients (ENGLISH)

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

**Alfred Ramani**(Ecole Polytechnique)Discrete Painlevé equations with periodic coefficients (ENGLISH)

[ Abstract ]

We present a series of results on discrete Painlevé equations with coefficients which are periodic functions of the independent variable. We show by explicit construction that for each affine Weyl group there exists an equation the coefficients of which have maximal periodicity. New results on equations associated to the affine Weyl group E_8 are also presented.

[ Reference URL ]We present a series of results on discrete Painlevé equations with coefficients which are periodic functions of the independent variable. We show by explicit construction that for each affine Weyl group there exists an equation the coefficients of which have maximal periodicity. New results on equations associated to the affine Weyl group E_8 are also presented.

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

#### Seminar on Geometric Complex Analysis

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

On a convex level set of a plurisubharmonic function and the support of the Monge-Ampere current (JAPANESE)

**Yusaku Tiba**(Tokyo Institute of Technology)On a convex level set of a plurisubharmonic function and the support of the Monge-Ampere current (JAPANESE)

[ Abstract ]

In this talk, we study a geometric property of a continuous plurisubharmonic function which is a solution of the Monge-Ampere equation and has a convex level set. By using our results and Lempert's results, we show a relation between the supports of the Monge-Ampere currents and complex $k$-extreme points of closed balls for the Kobayashi distance in a bounded convex domain in $C^n$.

In this talk, we study a geometric property of a continuous plurisubharmonic function which is a solution of the Monge-Ampere equation and has a convex level set. By using our results and Lempert's results, we show a relation between the supports of the Monge-Ampere currents and complex $k$-extreme points of closed balls for the Kobayashi distance in a bounded convex domain in $C^n$.

#### Classical Analysis

16:00-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY OF DYNAMICAL SYSTEMS

**Jean-Pierre RAMIS**(Toulouse)DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY OF DYNAMICAL SYSTEMS

[ Abstract ]

We will explain how to get obstructions to the integrability of analytic Hamiltonian Systems (in the classical Liouville sense) using Differential Galois Theory (introduced by Emile Picard at the end of XIX-th century). It is the so-called Morales-Ramis theory. Even if this sounds abstract, there exist efficient algorithms allowing to apply the theory and a lot of applications in various domains.

Firstly I will present basics on Hamiltonian Systems and integrability on one side and on Differential Galois Theory on the other side. Then I will state the main theorems. Afterwards I will describe some applications.

We will explain how to get obstructions to the integrability of analytic Hamiltonian Systems (in the classical Liouville sense) using Differential Galois Theory (introduced by Emile Picard at the end of XIX-th century). It is the so-called Morales-Ramis theory. Even if this sounds abstract, there exist efficient algorithms allowing to apply the theory and a lot of applications in various domains.

Firstly I will present basics on Hamiltonian Systems and integrability on one side and on Differential Galois Theory on the other side. Then I will state the main theorems. Afterwards I will describe some applications.

### 2014/11/07

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Harmonic maps into the hyperbolic plane and their applications to surface theory (Japanese)

**Shinpei KOBAYASHI**(Hokkaido University)Harmonic maps into the hyperbolic plane and their applications to surface theory (Japanese)

[ Abstract ]

Harmonic maps from two-dimensional Riemannian manifolds into the hyperbolic plane have been well studied. Since constant mean curvature surfaces in the Minkowski space have harmonic Gauss maps into the hyperbolic plane, there exist applications to surface theory.

In 1998, Dorfmeister, Pedit and Wu established the construction method of harmonic maps into symmetric spaces via loop group method. Recently, harmonic maps into the hyperbolic plane appear in various classes of surfaces, e.g., minimal surfaces in the Heisenberg group,

maximal surfaces in the anti-de Sitter space or constant Gaussian curvature surfaces in the hyperbolic space. In this talk I will talk about the general construction method of harmonic maps from surfaces into symmetric spaces via loop group method and the case of the hyperbolic plane in details.

Harmonic maps from two-dimensional Riemannian manifolds into the hyperbolic plane have been well studied. Since constant mean curvature surfaces in the Minkowski space have harmonic Gauss maps into the hyperbolic plane, there exist applications to surface theory.

In 1998, Dorfmeister, Pedit and Wu established the construction method of harmonic maps into symmetric spaces via loop group method. Recently, harmonic maps into the hyperbolic plane appear in various classes of surfaces, e.g., minimal surfaces in the Heisenberg group,

maximal surfaces in the anti-de Sitter space or constant Gaussian curvature surfaces in the hyperbolic space. In this talk I will talk about the general construction method of harmonic maps from surfaces into symmetric spaces via loop group method and the case of the hyperbolic plane in details.

### 2014/11/05

#### Operator Algebra Seminars

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

On the noncommutativity of the central sequence $C^*$-algebra $F(A)$ (ENGLISH)

**Hiroshi Ando**(Univ. Copenhagen)On the noncommutativity of the central sequence $C^*$-algebra $F(A)$ (ENGLISH)

#### Mathematical Biology Seminar

14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

Ecological conditions favoring budding in colonial organisms under environmental disturbance (JAPANESE)

[ Reference URL ]

https://sites.google.com/site/mayukonakamarulab/

**Mayuko Nakamaru**(Department of Value and Decision Science, Tokyo Institute of Technology)Ecological conditions favoring budding in colonial organisms under environmental disturbance (JAPANESE)

[ Reference URL ]

https://sites.google.com/site/mayukonakamarulab/

### 2014/11/04

#### Tuesday Seminar on Topology

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

The coarse geometry of Teichmuller space. (ENGLISH)

**Brian Bowditch**(University of Warwick)The coarse geometry of Teichmuller space. (ENGLISH)

[ Abstract ]

We describe some results regarding the coarse geometry of the

Teichmuller space

of a compact surface. In particular, we describe when the Teichmuller

space admits quasi-isometric embeddings of euclidean spaces and

half-spaces.

We also give some partial results regarding the quasi-isometric rigidity

of Teichmuller space. These results are based on the fact that Teichmuller

space admits a ternary operation, natural up to bounded distance

which endows it with the structure of a coarse median space.

We describe some results regarding the coarse geometry of the

Teichmuller space

of a compact surface. In particular, we describe when the Teichmuller

space admits quasi-isometric embeddings of euclidean spaces and

half-spaces.

We also give some partial results regarding the quasi-isometric rigidity

of Teichmuller space. These results are based on the fact that Teichmuller

space admits a ternary operation, natural up to bounded distance

which endows it with the structure of a coarse median space.

#### Seminar on Probability and Statistics

16:30-17:40 Room #052 (Graduate School of Math. Sci. Bldg.)

Conditions for consistency of a log-likelihood-based information criterion in normal multivariate linear regression models under the violation of normality assumption

**YANAGIHARA, Hirokazu**(Graduate School of Science, Hiroshima University)Conditions for consistency of a log-likelihood-based information criterion in normal multivariate linear regression models under the violation of normality assumption

### 2014/10/29

#### Operator Algebra Seminars

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

The classification of easy quantum groups (ENGLISH)

**Sven Raum**(RIMS, Kyoto Univ.)The classification of easy quantum groups (ENGLISH)

#### Lie Groups and Representation Theory

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

Harmonic analysis on reductive p-adic symmetric spaces. (ENGLISH)

**Patrick Delorme**(UER Scientifique de Luminy Universite d'Aix-Marseille II )Harmonic analysis on reductive p-adic symmetric spaces. (ENGLISH)

[ Abstract ]

In this lecture we will review the Plancherel formula that

we got by looking to neighborhoods at infinity of the

symmetric spaces and then using the method of Sakellaridis-Venkatesh

for spherical varieties for a split group. For us the group

is not necessarily split. We will try to show what questions

are raised by this work for real spherical varieties.

We will present in the last part a joint work with Pascale

Harinck and Yiannis Sakellaridis in which we prove Paley-Wiener

theorems for symmetric spaces.

In this lecture we will review the Plancherel formula that

we got by looking to neighborhoods at infinity of the

symmetric spaces and then using the method of Sakellaridis-Venkatesh

for spherical varieties for a split group. For us the group

is not necessarily split. We will try to show what questions

are raised by this work for real spherical varieties.

We will present in the last part a joint work with Pascale

Harinck and Yiannis Sakellaridis in which we prove Paley-Wiener

theorems for symmetric spaces.

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