## Seminar information archive

Seminar information archive ～09/18｜Today's seminar 09/19 | Future seminars 09/20～

#### Seminar on Probability and Statistics

14:50-16:00 Room #052 (Graduate School of Math. Sci. Bldg.)

LASSO に対する AIC タイプの情報量規準 (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/06.html

**NINOMIYA, Yoshiyuki**(Kyusyu University)LASSO に対する AIC タイプの情報量規準 (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/06.html

### 2013/11/08

#### Operator Algebra Seminars

10:00-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Introduction to the Ando-Haagerup theory IV (JAPANESE)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to the Ando-Haagerup theory IV (JAPANESE)

#### Colloquium

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

Ext Analogues of Branching laws (ENGLISH)

**Dipendra Prasad**(Tata Institute of Fundamental Research)Ext Analogues of Branching laws (ENGLISH)

[ Abstract ]

The decomposition of a representation of a group when restricted to a

subgroup is an important problem well-studied for finite and compact Lie

groups, and continues to be of much contemporary interest in the context

of real and $p$-adic groups. We will survey some of the questions that have

recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.

The decomposition of a representation of a group when restricted to a

subgroup is an important problem well-studied for finite and compact Lie

groups, and continues to be of much contemporary interest in the context

of real and $p$-adic groups. We will survey some of the questions that have

recently been considered, and look at a variation of these questions involving concepts in homological algebra which gives rise to interesting newer questions.

### 2013/11/07

#### Operator Algebra Seminars

15:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Introduction to the Ando-Haagerup theory III (JAPANESE)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to the Ando-Haagerup theory III (JAPANESE)

#### GCOE Seminars

17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)

Maximum Regularity Principle for Conservative Evolutionary Partial Dierential Equations (ENGLISH)

**Bingyu Zhang**(University of Cincinnati)Maximum Regularity Principle for Conservative Evolutionary Partial Dierential Equations (ENGLISH)

#### Lie Groups and Representation Theory

13:30-14:20 Room #000 (Graduate School of Math. Sci. Bldg.)

Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces (ENGLISH)

**Toshiyuki Kobayashi**(the University of Tokyo)Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces (ENGLISH)

[ Abstract ]

The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as an example, I plan to explain two programs:

1. (global shape) Exisitence problem of compact locally homogeneous spaces, and defomation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian, and its stability under the deformation of the geometric structure.

The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as an example, I plan to explain two programs:

1. (global shape) Exisitence problem of compact locally homogeneous spaces, and defomation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian, and its stability under the deformation of the geometric structure.

#### Lie Groups and Representation Theory

14:30-17:40 Room #000 (Graduate School of Math. Sci. Bldg.)

Weightless cohomology of algebraic varieties (ENGLISH)

Visible actions on generalized flag varieties

--- Geometry of multiplicity-free representations of $SO(N)$ (ENGLISH)

Holomorphic discrete series and Borel-de Siebenthal discrete series (ENGLISH)

Branching laws and the local Langlands correspondence (ENGLISH)

**Vaibhav Vaish**(the Institute of Mathematical Sciences) 14:30-15:20Weightless cohomology of algebraic varieties (ENGLISH)

[ Abstract ]

Using Morel's weight truncations in categories of mixed sheaves, we attach to any variety defined over complex numbers, over finite fields or even over a number field, a series of groups called the weightless cohomology groups. These lie between the usual cohomology and the intersection cohomology, have a natural ring structure, satisfy Kunneth, and are functorial for certain morphisms.

The construction is motivic and naturally arises in the context of Shimura Varieties where they capture the cohomology of Reductive Borel-Serre compactification. The construction also yields invariants of singularities associated with the combinatorics of the boundary divisors in any resolution.

Using Morel's weight truncations in categories of mixed sheaves, we attach to any variety defined over complex numbers, over finite fields or even over a number field, a series of groups called the weightless cohomology groups. These lie between the usual cohomology and the intersection cohomology, have a natural ring structure, satisfy Kunneth, and are functorial for certain morphisms.

The construction is motivic and naturally arises in the context of Shimura Varieties where they capture the cohomology of Reductive Borel-Serre compactification. The construction also yields invariants of singularities associated with the combinatorics of the boundary divisors in any resolution.

**Yuichiro Tanaka**(the University of Tokyo) 15:40-16:10Visible actions on generalized flag varieties

--- Geometry of multiplicity-free representations of $SO(N)$ (ENGLISH)

[ Abstract ]

The subject of study is tensor product representations of irreducible representations of the orthogonal group, which are multiplicity-free. Here we say a group representation is multiplicity-free if any irreducible representation occurs at most once in its irreducible decomposition.

The motivation is the theory of visible actions on complex manifolds, which was introduced by T. Kobayashi. In this theory, the main tool for proving the multiplicity-freeness property of group representations is the ``propagation theorem of the multiplicity-freeness property". By using this theorem and Stembridge's classification result, we obtain the following: All the multiplicity-free tensor product representations of $SO(N)$ and $Spin(N)$ can be obtained from character, alternating tensor product and spin representations combined with visible actions on orthogonal generalized flag varieties.

The subject of study is tensor product representations of irreducible representations of the orthogonal group, which are multiplicity-free. Here we say a group representation is multiplicity-free if any irreducible representation occurs at most once in its irreducible decomposition.

The motivation is the theory of visible actions on complex manifolds, which was introduced by T. Kobayashi. In this theory, the main tool for proving the multiplicity-freeness property of group representations is the ``propagation theorem of the multiplicity-freeness property". By using this theorem and Stembridge's classification result, we obtain the following: All the multiplicity-free tensor product representations of $SO(N)$ and $Spin(N)$ can be obtained from character, alternating tensor product and spin representations combined with visible actions on orthogonal generalized flag varieties.

**Pampa Paul**(Indian Statistical Institute, Kolkata) 16:10-16:40Holomorphic discrete series and Borel-de Siebenthal discrete series (ENGLISH)

[ Abstract ]

Let $G_0$ be a simply connected non-compact real simple Lie group with maximal compact subgroup $K_0$.

Let $T_0\\subset K_0$ be a Cartan subgroup of $K_0$ as well as of $G_0$. So $G_0$ has discrete series representations.

Denote by $\\frak{g}, \\frak{k},$ and $\\frak{t}$, the

complexifications of the Lie algebras $\\frak{g}_0, \\frak{k}_0$ and $\\frak{t}_0$ of $G_0, K_0$ and $T_0$ respectively.

There exists a positive root system $\\Delta^+$ of $\\frak{g}$ with respect to $\\frak{t}$, known as the Borel-de Siebenthal positive system for which there is exactly one non-compact simple root, denoted $\\nu$. Let $\\mu$ denote the highest root.

If $G_0/K_0$ is Hermitian symmetric, then $\\nu$ has coefficient $1$ in $\\mu$ and one can define holomorphic discrete series representation of $G_0$ using $\\Delta^+$.

If $G_0/K_0$ is not Hermitian symmetric, the coefficient of $\\nu$ in the highest root $\\mu$ is $2$.

In this case, Borel-de Siebenthal discrete series of $G_0$ is defined using $\\Delta^+$ in a manner analogous to the holomorphic discrete series.

Let $\\nu^*$ be the fundamental weight corresponding to $\\nu$ and $L_0$ be the centralizer in $K_0$ of the circle subgroup defined by $i\\nu^*$.

Note that $L_0 = K_0$, when $G_0/K_0$ is Hermitian symmetric. Otherwise, $L_0$ is a proper subgroup of $K_0$ and $K_0/L_0$ is an irreducible compact Hermitian symmetric space.

Let $G$ be the simply connected Lie group with Lie algebra $\\frak{g}$ and $K_0^* \\subset G$ be the dual of $K_0$ with respect to $L_0$ (or, the image of $L_0$ in $G$).

Then $K_0^*/L_0$ is an irreducible non-compact Hermitian symmetric space dual to $K_0/L_0$.

In this talk, to each Borel-de Siebenthal discrete series of $G_0$, a holomorphic discrete series of $K_0^*$ will be associated and occurrence of common $L_0$-types in both the series will be discussed.

Let $G_0$ be a simply connected non-compact real simple Lie group with maximal compact subgroup $K_0$.

Let $T_0\\subset K_0$ be a Cartan subgroup of $K_0$ as well as of $G_0$. So $G_0$ has discrete series representations.

Denote by $\\frak{g}, \\frak{k},$ and $\\frak{t}$, the

complexifications of the Lie algebras $\\frak{g}_0, \\frak{k}_0$ and $\\frak{t}_0$ of $G_0, K_0$ and $T_0$ respectively.

There exists a positive root system $\\Delta^+$ of $\\frak{g}$ with respect to $\\frak{t}$, known as the Borel-de Siebenthal positive system for which there is exactly one non-compact simple root, denoted $\\nu$. Let $\\mu$ denote the highest root.

If $G_0/K_0$ is Hermitian symmetric, then $\\nu$ has coefficient $1$ in $\\mu$ and one can define holomorphic discrete series representation of $G_0$ using $\\Delta^+$.

If $G_0/K_0$ is not Hermitian symmetric, the coefficient of $\\nu$ in the highest root $\\mu$ is $2$.

In this case, Borel-de Siebenthal discrete series of $G_0$ is defined using $\\Delta^+$ in a manner analogous to the holomorphic discrete series.

Let $\\nu^*$ be the fundamental weight corresponding to $\\nu$ and $L_0$ be the centralizer in $K_0$ of the circle subgroup defined by $i\\nu^*$.

Note that $L_0 = K_0$, when $G_0/K_0$ is Hermitian symmetric. Otherwise, $L_0$ is a proper subgroup of $K_0$ and $K_0/L_0$ is an irreducible compact Hermitian symmetric space.

Let $G$ be the simply connected Lie group with Lie algebra $\\frak{g}$ and $K_0^* \\subset G$ be the dual of $K_0$ with respect to $L_0$ (or, the image of $L_0$ in $G$).

Then $K_0^*/L_0$ is an irreducible non-compact Hermitian symmetric space dual to $K_0/L_0$.

In this talk, to each Borel-de Siebenthal discrete series of $G_0$, a holomorphic discrete series of $K_0^*$ will be associated and occurrence of common $L_0$-types in both the series will be discussed.

**Dipendra Prasad**(Tata Institute of Fundamental Research) 16:50-17:40Branching laws and the local Langlands correspondence (ENGLISH)

[ Abstract ]

The decomposition of a representation of a group when restricted to a subgroup is an important problem well-studied for finite and compact Lie groups, and continues to be of much contemporary interest in the context of real and $p$-adic groups. We will survey some of the questions that have recently been considered drawing analogy with Compact Lie groups, and what it suggests in the context of real and $p$-adic groups via what is called the local Langlands correspondence.

The decomposition of a representation of a group when restricted to a subgroup is an important problem well-studied for finite and compact Lie groups, and continues to be of much contemporary interest in the context of real and $p$-adic groups. We will survey some of the questions that have recently been considered drawing analogy with Compact Lie groups, and what it suggests in the context of real and $p$-adic groups via what is called the local Langlands correspondence.

### 2013/11/06

#### Operator Algebra Seminars

10:00-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Introduction to the Ando-Haagerup theory II (JAPANESE)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to the Ando-Haagerup theory II (JAPANESE)

### 2013/11/05

#### Tuesday Seminar on Topology

16:30-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The isotopy problem of non-singular closed 1-forms. (ENGLISH)

**Carlos Moraga Ferrandiz**(The University of Tokyo, JSPS)The isotopy problem of non-singular closed 1-forms. (ENGLISH)

[ Abstract ]

Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.

A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.

The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.

Given alpha_0, alpha_1 two cohomologous non-singular closed 1-forms of a compact manifold M, are they always isotopic? We expect a negative answer to this question, at least in high dimensions by the work of Laudenbach, as well as an obstruction living in the algebraic K-theory of the Novikov ring associated to the underlying cohomology class.

A similar problem for functions N x [0,1] --> [0,1] without critical points was treated by Hatcher and Wagoner in the 70s.

The first goal of this talk is to explain how we can carry a part of the strategy of Hatcher and Wagoner into the context of closed 1-forms and to indicate the main difficulties that appear by doing so. The second goal is to show the techniques to treat this difficulties and the progress in defining the expected obstruction.

#### Operator Algebra Seminars

15:30-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)

Introduction to the Ando-Haagerup theory I (JAPANESE)

**Reiji Tomatsu**(Hokkaido Univ.)Introduction to the Ando-Haagerup theory I (JAPANESE)

### 2013/10/30

#### Operator Algebra Seminars

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

Amenable minimal Cantor systems of free groups arising from

diagonal actions (JAPANESE)

**Yuhei Suzuki**(Univ. Tokyo)Amenable minimal Cantor systems of free groups arising from

diagonal actions (JAPANESE)

#### Number Theory Seminar

16:40-17:40 Room #002 (Graduate School of Math. Sci. Bldg.)

Explicit integral cocycles on GLn and special values of p-adic partial zeta functions (ENGLISH)

**Pierre Charollois**(Université Paris 6)Explicit integral cocycles on GLn and special values of p-adic partial zeta functions (ENGLISH)

[ Abstract ]

Building on earlier work by Sczech, we contruct an explicit integral valued cocycle on GLn(Z).

It allows for the detailed analysis of the order of vanishing and of the special value at s=0 of the p-adic partial zeta functions introduced by Pi. Cassou-Noguès and Deligne-Ribet. In particular we recover a result of Wiles (1990) on Gross conjecture.

Another construction, now based on Shintani's method, is shown to lead to a cohomologous cocycle. This is joint work with S. Dasgupta and M. Greenberg.

Building on earlier work by Sczech, we contruct an explicit integral valued cocycle on GLn(Z).

It allows for the detailed analysis of the order of vanishing and of the special value at s=0 of the p-adic partial zeta functions introduced by Pi. Cassou-Noguès and Deligne-Ribet. In particular we recover a result of Wiles (1990) on Gross conjecture.

Another construction, now based on Shintani's method, is shown to lead to a cohomologous cocycle. This is joint work with S. Dasgupta and M. Greenberg.

#### Classical Analysis

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

The space of monodromy and Stokes data for q-difference equations (ENGLISH)

**Jacques Sauloy**(Institute de Mathematiques de Toulouse, Universite Paul Sabatier)The space of monodromy and Stokes data for q-difference equations (ENGLISH)

[ Abstract ]

Riemann-Hilbert correspondance for fuchsian q-difference equations has been obtained by Sauloy along the lines of Birkhoff and then, for irregular equations, by Ramis, Sauloy and Zhang in terms of q-Stokes operators.

However, these correspondances are not formulated in geometric terms, which makes them little suitable for the study of isomonodromy or "iso-Stokes" deformations. Recently, under the impulse of Ohyama, we started to construct such a geometric description in order to apply it to the famous work of Jimbo-Sakai and then to more recent extensions. I shall describe this work.

Riemann-Hilbert correspondance for fuchsian q-difference equations has been obtained by Sauloy along the lines of Birkhoff and then, for irregular equations, by Ramis, Sauloy and Zhang in terms of q-Stokes operators.

However, these correspondances are not formulated in geometric terms, which makes them little suitable for the study of isomonodromy or "iso-Stokes" deformations. Recently, under the impulse of Ohyama, we started to construct such a geometric description in order to apply it to the famous work of Jimbo-Sakai and then to more recent extensions. I shall describe this work.

### 2013/10/29

#### Tuesday Seminar on Topology

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

Fundamental groups of algebraic varieties (ENGLISH)

**Daniel Matei**(IMAR, Bucharest)Fundamental groups of algebraic varieties (ENGLISH)

[ Abstract ]

We discuss restrictions imposed by the complex

structure on fundamental groups of quasi-projective

algebraic varieties with mild singularities.

We investigate quasi-projectivity of various geometric

classes of finitely presented groups.

We discuss restrictions imposed by the complex

structure on fundamental groups of quasi-projective

algebraic varieties with mild singularities.

We investigate quasi-projectivity of various geometric

classes of finitely presented groups.

#### Numerical Analysis Seminar

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

Development of multi-dimensional compact difference formulas with the aid of formula manipulation software (JAPANESE)

[ Reference URL ]

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

**Sei-ichiro Nagoya**(ARK Information Systems)Development of multi-dimensional compact difference formulas with the aid of formula manipulation software (JAPANESE)

[ Reference URL ]

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

#### Lie Groups and Representation Theory

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

Geometry of multiplicity-free representations of SO(N) and visible actions (JAPANESE)

**Yuichiro Tanaka**(the University of Tokyo, Graduate School of Mathematical Sciences)Geometry of multiplicity-free representations of SO(N) and visible actions (JAPANESE)

[ Abstract ]

For a connected compact simple Lie group of type B or D,

we find pairs $(V_{1},V_{2})$ of irreducible representations of G such that the tensor product representation $V_{1}¥otimes V_{2}$ is multiplicity-free by a geometric consideration based on

a notion of visible actions on complex manifolds,

introduced by T. Kobayashi. The pairs we find exhaust

all the multiplicity-free pairs by an earlier

combinatorial classification due to Stembridge.

For a connected compact simple Lie group of type B or D,

we find pairs $(V_{1},V_{2})$ of irreducible representations of G such that the tensor product representation $V_{1}¥otimes V_{2}$ is multiplicity-free by a geometric consideration based on

a notion of visible actions on complex manifolds,

introduced by T. Kobayashi. The pairs we find exhaust

all the multiplicity-free pairs by an earlier

combinatorial classification due to Stembridge.

### 2013/10/28

#### Seminar on Geometric Complex Analysis

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

Minimal singular metrics of a line bundle admitting no Zariski decomposition (JAPANESE)

**Takayuki Koike**(The University of Tokyo)Minimal singular metrics of a line bundle admitting no Zariski decomposition (JAPANESE)

[ Abstract ]

We give a concrete expression of a minimal singular metric of a big line bundle on a compact Kähler manifold which is the total space of a toric bundle over a complex torus. In this class of manifolds, Nakayama constructed examples which have line bundles admitting no Zariski decomposition even after any proper modifications. As an application, we discuss the Zariski closedness of non-nef loci and the openness conjecture of Demailly and Kollar in this class.

We give a concrete expression of a minimal singular metric of a big line bundle on a compact Kähler manifold which is the total space of a toric bundle over a complex torus. In this class of manifolds, Nakayama constructed examples which have line bundles admitting no Zariski decomposition even after any proper modifications. As an application, we discuss the Zariski closedness of non-nef loci and the openness conjecture of Demailly and Kollar in this class.

#### Algebraic Geometry Seminar

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

Weak Borisov-Alexeev-Borisov conjecture for 3-fold Mori Fiber spaces (ENGLISH)

**Chen Jiang**(University of Tokyo)Weak Borisov-Alexeev-Borisov conjecture for 3-fold Mori Fiber spaces (ENGLISH)

[ Abstract ]

We investigate $\\epsilon$-klt log Fano 3-folds with some Mori fiber space structure, more precisely, with a del Pezzo fibration structure, or a conic bundle structure over projective plane. We give a bound for the log anti-canonical volume of such pair. The method is constructing non-klt centers and using connectedness lemma. This result is related to birational boundedness of log Fano varieties.

We investigate $\\epsilon$-klt log Fano 3-folds with some Mori fiber space structure, more precisely, with a del Pezzo fibration structure, or a conic bundle structure over projective plane. We give a bound for the log anti-canonical volume of such pair. The method is constructing non-klt centers and using connectedness lemma. This result is related to birational boundedness of log Fano varieties.

### 2013/10/25

#### Seminar on Probability and Statistics

14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)

Sparse coding and structured dictionary learning (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/05.html

**MURATA, Noboru**(Waseda University)Sparse coding and structured dictionary learning (JAPANESE)

[ Reference URL ]

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/05.html

### 2013/10/24

#### Geometry Colloquium

10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)

Some Uniqueness Theorems for Smoothing Singularities in Special Lagrangian Geometry (JAPANESE)

**Yohsuke Imagi**(Kyoto University)Some Uniqueness Theorems for Smoothing Singularities in Special Lagrangian Geometry (JAPANESE)

[ Abstract ]

Special Lagrangian submanifolds are area-minimizing Lagrangian submanifolds of Calabi--Yau manifolds. I'll talk mainly about the singularities of two special Lagrangian planes intersecting transversely. I'll determine a class of smoothing models for the singularities.

By some results of Abouzaid and Smith one can determine the smoothing models up to quasi-isomorphism in a Fukaya category. I'll combine it with a technique of Thomas and Yau.

Special Lagrangian submanifolds are area-minimizing Lagrangian submanifolds of Calabi--Yau manifolds. I'll talk mainly about the singularities of two special Lagrangian planes intersecting transversely. I'll determine a class of smoothing models for the singularities.

By some results of Abouzaid and Smith one can determine the smoothing models up to quasi-isomorphism in a Fukaya category. I'll combine it with a technique of Thomas and Yau.

### 2013/10/23

#### Operator Algebra Seminars

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

Classification of quantum homogeneous spaces (ENGLISH)

**Makoto Yamashita**(Ochanomizu Univ.)Classification of quantum homogeneous spaces (ENGLISH)

#### Seminar on Probability and Statistics

13:00-15:30 Room #006 (Graduate School of Math. Sci. Bldg.)

Limit theorems for ambit processes (ENGLISH)

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/04.html

**Mark Podolskij**(Universität Heidelberg)Limit theorems for ambit processes (ENGLISH)

[ Abstract ]

We present some recent limit theorems for high frequency observations of ambit processes. Ambit processes constitute a flexible class of models, which are usually used to describe turbulent motion in physics. Mathematically speaking, they have a continuous moving average structure with additional random component called intermittency. In the first part of the lecture we will demonstrate the asymptotic theory for ambit processes driven by Brownian motion. The second part will deal with Levy driven ambit processes. We will see that these two cases deliver completely different limiting results.

本講演は数物フロンティア・リーディング大学院のレクチャーとして行います.

[ Reference URL ]We present some recent limit theorems for high frequency observations of ambit processes. Ambit processes constitute a flexible class of models, which are usually used to describe turbulent motion in physics. Mathematically speaking, they have a continuous moving average structure with additional random component called intermittency. In the first part of the lecture we will demonstrate the asymptotic theory for ambit processes driven by Brownian motion. The second part will deal with Levy driven ambit processes. We will see that these two cases deliver completely different limiting results.

本講演は数物フロンティア・リーディング大学院のレクチャーとして行います.

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2013/04.html

### 2013/10/22

#### PDE Real Analysis Seminar

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

Fractional harmonic maps and applications (ENGLISH)

**Armin Schikorra**(MPI for Mathematics in the Sciences, Leipzig)Fractional harmonic maps and applications (ENGLISH)

[ Abstract ]

Fractional harmonic mappings are critical points of a generalized Dirichlet Energy where the gradient is replaced with a (non-local) differential operator.

I will present aspects of the regularity theory of (non-local) fractional harmonic maps into manifolds, which extends (and contains) the theory of (poly-)harmonic mappings.

I also will mention, how one can show regularity for critical points of the Moebius (Knot-) Energy, applying the techniques developed in this theory.

Fractional harmonic mappings are critical points of a generalized Dirichlet Energy where the gradient is replaced with a (non-local) differential operator.

I will present aspects of the regularity theory of (non-local) fractional harmonic maps into manifolds, which extends (and contains) the theory of (poly-)harmonic mappings.

I also will mention, how one can show regularity for critical points of the Moebius (Knot-) Energy, applying the techniques developed in this theory.

#### Tuesday Seminar on Topology

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

Cluster algebra and complex volume of knots (JAPANESE)

**Rei Inoue**(Chiba University)Cluster algebra and complex volume of knots (JAPANESE)

[ Abstract ]

The cluster algebra was introduced by Fomin and Zelevinsky around

2000. The characteristic operation in the algebra called `mutation' is

related to various notions in mathematics and mathematical physics. In

this talk I review a basics of the cluster algebra, and introduce its

application to study the complex volume of knot complements in S^3.

Here a mutation corresponds to an ideal tetrahedron.

This talk is based on joint work with Kazuhiro Hikami (Kyushu University).

The cluster algebra was introduced by Fomin and Zelevinsky around

2000. The characteristic operation in the algebra called `mutation' is

related to various notions in mathematics and mathematical physics. In

this talk I review a basics of the cluster algebra, and introduce its

application to study the complex volume of knot complements in S^3.

Here a mutation corresponds to an ideal tetrahedron.

This talk is based on joint work with Kazuhiro Hikami (Kyushu University).

#### Lie Groups and Representation Theory

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

Representation Theory and Microlocal Analysis (ENGLISH)

**Benjamin Harris**(Louisiana State University (USA))Representation Theory and Microlocal Analysis (ENGLISH)

[ Abstract ]

Suppose $H\\subset K$ are compact, connected Lie groups, and suppose $\\tau$ is an irreducible, unitary representation of $H$. In 1979, Kashiwara and Vergne proved a simple asymptotic formula for the decomposition of $Ind_H^K\\tau$ by microlocally studying the regularity of vectors in this representation, thought of as vector valued functions on $K$. In 1998, Kobayashi proved a powerful criterion for the discrete decomposability of an irreducible, unitary representation $\\pi$ of a reductive Lie group $G$ when restricted to a reductive subgroup $H$. One of his key ideas was to restrict $\\pi$ to a representation of a maximal compact subgroup $K\\subset G$, view $\\pi$ as a subrepresentation of $L^2(K)$, and then use ideas similar to those developed by Kashiwara and Vergne.

In a recent preprint the speaker wrote with Hongyu He and Gestur Olafsson, the authors consider the possibility of studying induction and restriction to a reductive Lie group $G$ by microlocally studying the regularity of the matrix coefficients of (possibly reducible) unitary representations of $G$, viewed as continuous functions on the (possibly noncompact) Lie group $G$. In this talk, we will outline the main results of this paper and give additional conjectures.

Suppose $H\\subset K$ are compact, connected Lie groups, and suppose $\\tau$ is an irreducible, unitary representation of $H$. In 1979, Kashiwara and Vergne proved a simple asymptotic formula for the decomposition of $Ind_H^K\\tau$ by microlocally studying the regularity of vectors in this representation, thought of as vector valued functions on $K$. In 1998, Kobayashi proved a powerful criterion for the discrete decomposability of an irreducible, unitary representation $\\pi$ of a reductive Lie group $G$ when restricted to a reductive subgroup $H$. One of his key ideas was to restrict $\\pi$ to a representation of a maximal compact subgroup $K\\subset G$, view $\\pi$ as a subrepresentation of $L^2(K)$, and then use ideas similar to those developed by Kashiwara and Vergne.

In a recent preprint the speaker wrote with Hongyu He and Gestur Olafsson, the authors consider the possibility of studying induction and restriction to a reductive Lie group $G$ by microlocally studying the regularity of the matrix coefficients of (possibly reducible) unitary representations of $G$, viewed as continuous functions on the (possibly noncompact) Lie group $G$. In this talk, we will outline the main results of this paper and give additional conjectures.

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