## Seminar information archive

Seminar information archive ～11/15｜Today's seminar 11/16 | Future seminars 11/17～

### 2013/01/22

#### Lie Groups and Representation Theory

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

Representation theory of finite W-algebras (ENGLISH)

**Simon Goodwin**(Birmingham University)Representation theory of finite W-algebras (ENGLISH)

[ Abstract ]

There has been a great deal of recent research interest in finite W-algebras motivated by important connection with primitive ideals of universal enveloping algebras and applications in mathematical physics.

There have been significant breakthroughs in the rerpesentation theory of finite W-algebras due to the research of a variety of mathematicians.

In this talk, we will give an overview of the representation theory of finite W-algebras focussing on W-algebras associated to classical Lie algebras (joint with J. Brown) and W-algebras associated to general linear Lie superalgebras (joint with J. Brown and J. Brundan).

There has been a great deal of recent research interest in finite W-algebras motivated by important connection with primitive ideals of universal enveloping algebras and applications in mathematical physics.

There have been significant breakthroughs in the rerpesentation theory of finite W-algebras due to the research of a variety of mathematicians.

In this talk, we will give an overview of the representation theory of finite W-algebras focussing on W-algebras associated to classical Lie algebras (joint with J. Brown) and W-algebras associated to general linear Lie superalgebras (joint with J. Brown and J. Brundan).

#### Tuesday Seminar on Topology

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

On the autonomous metric of the area preserving diffeomorphism

of the two dimensional disc. (ENGLISH)

**Jarek Kedra**(University of Aberdeen)On the autonomous metric of the area preserving diffeomorphism

of the two dimensional disc. (ENGLISH)

[ Abstract ]

Let D be the open unit disc in the Euclidean plane and let

G:=Diff(D, area) be the group of smooth compactly supported

area-preserving diffeomorphisms of D. A diffeomorphism is called

autonomous if it is the time one map of the flow of a time independent

vector field. Every diffeomorphism in G is a composition of a number

of autonomous diffeomorphisms. The least amount of such

diffeomorphisms defines a norm on G. In the talk I will investigate

geometric properties of such a norm.

In particular I will construct a bi-Lipschitz embedding of the free

abelian group of arbitrary rank to G. I will also show that the space

of homogeneous quasi-morphisms vanishing on all autonomous

diffeomorphisms in G is infinite dimensional.

This is a joint work with Michael Brandenbursky.

Let D be the open unit disc in the Euclidean plane and let

G:=Diff(D, area) be the group of smooth compactly supported

area-preserving diffeomorphisms of D. A diffeomorphism is called

autonomous if it is the time one map of the flow of a time independent

vector field. Every diffeomorphism in G is a composition of a number

of autonomous diffeomorphisms. The least amount of such

diffeomorphisms defines a norm on G. In the talk I will investigate

geometric properties of such a norm.

In particular I will construct a bi-Lipschitz embedding of the free

abelian group of arbitrary rank to G. I will also show that the space

of homogeneous quasi-morphisms vanishing on all autonomous

diffeomorphisms in G is infinite dimensional.

This is a joint work with Michael Brandenbursky.

### 2013/01/21

#### Tuesday Seminar on Topology

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

)

Lie foliations transversely modeled on nilpotent Lie

algebras

(JAPANESE)

**Naoki Kato**(The University of Tokyo)

Lie foliations transversely modeled on nilpotent Lie

algebras

(JAPANESE)

[ Abstract ]

To each Lie $\\mathfrak{g}$-foliation, there is an associated subalgebra

$\\mathfrak{h}$ of $\\mathfrak{g}$ with the foliation, which is called the

structure Lie algabra. In this talk, we will explain the inverse problem,

that is, which pair $(\\mathfrak{g},\\mathfrak{h})$ can be realized as a

Lie $\\mathfrak{g}$-foliation with the structure Lie algabra $\\mathfrak{h}

$, under the assumption that $\\mathfrak{g}$ is nilpotent.

To each Lie $\\mathfrak{g}$-foliation, there is an associated subalgebra

$\\mathfrak{h}$ of $\\mathfrak{g}$ with the foliation, which is called the

structure Lie algabra. In this talk, we will explain the inverse problem,

that is, which pair $(\\mathfrak{g},\\mathfrak{h})$ can be realized as a

Lie $\\mathfrak{g}$-foliation with the structure Lie algabra $\\mathfrak{h}

$, under the assumption that $\\mathfrak{g}$ is nilpotent.

#### Tuesday Seminar on Topology

17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

Quasi-morphisms on the group of area-preserving diffeomorphisms of

the 2-disk

(JAPANESE)

**Tomohiko Ishida**(The University of Tokyo)Quasi-morphisms on the group of area-preserving diffeomorphisms of

the 2-disk

(JAPANESE)

[ Abstract ]

Gambaudo and Ghys constructed linearly independent countably many quasi-

morphisms on the group of area-preserving diffeomorphisms of the 2-disk

from quasi-morphisms on braid groups.

In this talk, we will explain that their construction is injective as a

homomorphism between vector spaces of quasi-morphisms.

If time permits, we introduce an application by Brandenbursky and K\\c{e}

dra.

Gambaudo and Ghys constructed linearly independent countably many quasi-

morphisms on the group of area-preserving diffeomorphisms of the 2-disk

from quasi-morphisms on braid groups.

In this talk, we will explain that their construction is injective as a

homomorphism between vector spaces of quasi-morphisms.

If time permits, we introduce an application by Brandenbursky and K\\c{e}

dra.

#### Seminar on Geometric Complex Analysis

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

Value distribution of meromorphic mappings to compact complex manifolds (JAPANESE)

**Takushi AMEMIYA**(MS U-Tokyo)Value distribution of meromorphic mappings to compact complex manifolds (JAPANESE)

[ Abstract ]

In a late paper of J. Noguchi and J. Winkelmann they showed the condition of being Kähler or non-Kähler of the image space to make a difference in the value distribution theory of meromorphic mappings into compact complex manifolds. In the present talk, we will discuss the order of meromorphic mappings to a Hopf surface which is more general than dealt with by Noguchi-Winkelmann, and an Inoue surface (they are non-Kähler surfaces). For a general Hopf surface $S$, we prove that there exists a differentiably non-degenerate holomorphic mapping $f:\mathbf{C}^2 \to S$ whose order satisfies $\rho_{f}\leq 1$. For an Inoue surface $S'$, we prove that every non-constant meromorphic mapping $f:\mathbf{C}^n \to S'$ is holomorphic and its order satisfies $\rho_{f}\geq 2$.

In a late paper of J. Noguchi and J. Winkelmann they showed the condition of being Kähler or non-Kähler of the image space to make a difference in the value distribution theory of meromorphic mappings into compact complex manifolds. In the present talk, we will discuss the order of meromorphic mappings to a Hopf surface which is more general than dealt with by Noguchi-Winkelmann, and an Inoue surface (they are non-Kähler surfaces). For a general Hopf surface $S$, we prove that there exists a differentiably non-degenerate holomorphic mapping $f:\mathbf{C}^2 \to S$ whose order satisfies $\rho_{f}\leq 1$. For an Inoue surface $S'$, we prove that every non-constant meromorphic mapping $f:\mathbf{C}^n \to S'$ is holomorphic and its order satisfies $\rho_{f}\geq 2$.

### 2013/01/16

#### Geometry Colloquium

10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)

A construction of Spin(7)-instantons (JAPANESE)

**Yuuji Tanaka**(Kyoto University)A construction of Spin(7)-instantons (JAPANESE)

[ Abstract ]

Spin(7)-instantons are elliptic gauge fields on 8-dimensional Spin(7)-manifolds, which minimize the Yang-Mills action. Analytic properties of Spin(7)-instantons have been studied by Gang Tian and others, but little was known about the existence of examples of Spin(7)-instantons other than an Oxford Ph.D thesis by Christopher Lewis in 1998.

There are two known constructions of compact Spin(7)-manifolds both obtained by Dominic Joyce. The first one begins with a torus orbifold of a special kind with non-isolated singularities. The Spin(7)-manifold is obtained by resolving the singularities with the aid of algebraic geometry techniques. The second one begins with a Calabi-Yau four-orbifold with isolated singular points of a special kind and an anti-holomorphic involution fixing only the singular points. The Spin(7)-manifold is obtained by gluing ALE Spin(7)-manifolds with anti-holomorphic involutions fixing only the origins to each singular point.

Christopher Lewis studied the problem of constructing Spin(7)-instantons on Spin(7)-manifolds coming from Joyce's first construction.

This talk describes a general construction of Spin(7)-instantons on examples of compact Spin(7)-manifolds coming from Joyce's second construction. Starting with certain Hermitian-Einstein connections on the Calabi-Yau four-orbifold and on ALE Spin(7)-manifolds, we glue them together simultaneously with the underlying pieces to make a Spin(7)-instanton on the compact Spin(7)-manifold by Joyce.

Spin(7)-instantons are elliptic gauge fields on 8-dimensional Spin(7)-manifolds, which minimize the Yang-Mills action. Analytic properties of Spin(7)-instantons have been studied by Gang Tian and others, but little was known about the existence of examples of Spin(7)-instantons other than an Oxford Ph.D thesis by Christopher Lewis in 1998.

There are two known constructions of compact Spin(7)-manifolds both obtained by Dominic Joyce. The first one begins with a torus orbifold of a special kind with non-isolated singularities. The Spin(7)-manifold is obtained by resolving the singularities with the aid of algebraic geometry techniques. The second one begins with a Calabi-Yau four-orbifold with isolated singular points of a special kind and an anti-holomorphic involution fixing only the singular points. The Spin(7)-manifold is obtained by gluing ALE Spin(7)-manifolds with anti-holomorphic involutions fixing only the origins to each singular point.

Christopher Lewis studied the problem of constructing Spin(7)-instantons on Spin(7)-manifolds coming from Joyce's first construction.

This talk describes a general construction of Spin(7)-instantons on examples of compact Spin(7)-manifolds coming from Joyce's second construction. Starting with certain Hermitian-Einstein connections on the Calabi-Yau four-orbifold and on ALE Spin(7)-manifolds, we glue them together simultaneously with the underlying pieces to make a Spin(7)-instanton on the compact Spin(7)-manifold by Joyce.

#### Number Theory Seminar

18:00-19:00 Room #002 (Graduate School of Math. Sci. Bldg.)

On differential modules associated to de Rham representations in the imperfect residue field case (ENGLISH)

**Shun Ohkubo**(University of Tokyo)On differential modules associated to de Rham representations in the imperfect residue field case (ENGLISH)

[ Abstract ]

Let K be a CDVF of mixed characteristic (0,p) and G the absolute Galois group of K. When the residue field of K is perfect, Laurent Berger constructed a p-adic differential equation N_dR(V) for any de Rham representation V of G. In this talk, we will generalize his construction when the residue field of K is not perfect. We also explain some ramification properties of our N_dR, which are due to Adriano Marmora in the perfect residue field case.

Let K be a CDVF of mixed characteristic (0,p) and G the absolute Galois group of K. When the residue field of K is perfect, Laurent Berger constructed a p-adic differential equation N_dR(V) for any de Rham representation V of G. In this talk, we will generalize his construction when the residue field of K is not perfect. We also explain some ramification properties of our N_dR, which are due to Adriano Marmora in the perfect residue field case.

#### Lectures

10:00-11:00 Room #123 (Graduate School of Math. Sci. Bldg.)

$W^*$-superrigidity of mixing Gaussian actions of rigid groups (ENGLISH)

**R\'emi Boutonnet**(ENS Lyon)$W^*$-superrigidity of mixing Gaussian actions of rigid groups (ENGLISH)

#### Lectures

11:30-12:30 Room #123 (Graduate School of Math. Sci. Bldg.)

The Approximation Property for Lie groups (ENGLISH)

**Tim de Laat**(University of Copenhagen)The Approximation Property for Lie groups (ENGLISH)

#### Lectures

14:40-15:40 Room #118 (Graduate School of Math. Sci. Bldg.)

Unique Cartan decomposition for II$_1$ factors arising from cross section equivalence relations (ENGLISH)

**Arnaud Brothier**(KU Leuven)Unique Cartan decomposition for II$_1$ factors arising from cross section equivalence relations (ENGLISH)

#### Lectures

15:55-16:55 Room #118 (Graduate School of Math. Sci. Bldg.)

Rigid $C^*$ tensor categories of bimodules over interpolated

free group factors (ENGLISH)

**Michael Hartglass**(UC Berkeley)Rigid $C^*$ tensor categories of bimodules over interpolated

free group factors (ENGLISH)

#### Lectures

17:10-18:10 Room #118 (Graduate School of Math. Sci. Bldg.)

Manifestly unitary conformal field theory (ENGLISH)

**James Tener**(UC Berkeley)Manifestly unitary conformal field theory (ENGLISH)

#### GCOE Seminars

14:40-15:40 Room #118 (Graduate School of Math. Sci. Bldg.)

Unique Cartan decomposition for II$_1$ factors arising from cross section equivalence relations (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-2.htm

**Arnaud Brothier**(KU Leuven)Unique Cartan decomposition for II$_1$ factors arising from cross section equivalence relations (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-2.htm

#### GCOE Seminars

15:55-16:55 Room #118 (Graduate School of Math. Sci. Bldg.)

TBA (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-2.htm

**Michael Hartglass**(UC Berkeley)TBA (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-2.htm

#### GCOE Seminars

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

3-D Calderon's Problem with partial Dirichlet-to Neumann map (ENGLISH)

**Oleg Emanouilov**(Colorado State University)3-D Calderon's Problem with partial Dirichlet-to Neumann map (ENGLISH)

[ Abstract ]

We present new results for the uniqueness of recovery of a potential in three dimensional Calderon's problem with partial Dirichlet-to-Neumann map.

The proof is based on complex geometric optics solutions and the Radon transform.

We present new results for the uniqueness of recovery of a potential in three dimensional Calderon's problem with partial Dirichlet-to-Neumann map.

The proof is based on complex geometric optics solutions and the Radon transform.

### 2013/01/15

#### Mathematical Biology Seminar

14:00-16:00 Room #152 (Graduate School of Math. Sci. Bldg.)

Bolyai Institute, University of Szeged)

Differential equation models describing cell proliferation process and their dynamics (JAPANESE)

**Yukihiko Nakata**(Bolyai Institute, University of Szeged)

Differential equation models describing cell proliferation process and their dynamics (JAPANESE)

#### Numerical Analysis Seminar

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

On the rigorous numerical verification of saddle-saddle connections (JAPANESE)

[ Reference URL ]

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

**Kaname Matsue**(Tohoku University)On the rigorous numerical verification of saddle-saddle connections (JAPANESE)

[ Reference URL ]

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

#### Mathematical Biology Seminar

14:00-16:00 Room #152 (Graduate School of Math. Sci. Bldg.)

Formulation of transient amplifying cell population growth process based on generation progression models (JAPANESE)

**Shinji Nakaoka**(RIKEN)Formulation of transient amplifying cell population growth process based on generation progression models (JAPANESE)

#### Algebraic Geometry Seminar

15:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Three Dimensional Birational Geoemtry--updates and problems (ENGLISH)

**Jungkai Alfred Chen**(National Taiwan University)Three Dimensional Birational Geoemtry--updates and problems (ENGLISH)

[ Abstract ]

In this talk I will talk about some recent results on

biratioanl classification and biratioanl geoemtry of threefolds.

Given a threefold of general type, we improved our previous result by

showing that $Vol \\ge 1/1680$ and $|mK_X|$ is biratioanl for $m \\ge

61$.

Compare with the worst known example that $X_{46} \\subset

\\mathbb{P}(4,5,6,7,23)$, one also knows that there are only finiteley

many singularities type

for threefolds of general type with $1/1680 \\le Vol \\le 1/420$. It is

then intereting to study threefolds of general type with given basket

of singularities and with given fiber structure.

Concerning threefolds with intermediate Kodaira dimension, we

considered the effective Iitaka fibration. For this purpose, it is

interesting to study threefolds with $\\kappa=1$ with given basket of

singularities and abelian fibration.

For explicit birational geoemtry, we will show our result that each

biratioanl map in minimal model program can be factored into a

sequence of following maps (or its inverse)

1. a divisorial contraction to a point of index r with discrepancy 1/r.

2. a blowup along a smooth curve

3. a flop

In this talk I will talk about some recent results on

biratioanl classification and biratioanl geoemtry of threefolds.

Given a threefold of general type, we improved our previous result by

showing that $Vol \\ge 1/1680$ and $|mK_X|$ is biratioanl for $m \\ge

61$.

Compare with the worst known example that $X_{46} \\subset

\\mathbb{P}(4,5,6,7,23)$, one also knows that there are only finiteley

many singularities type

for threefolds of general type with $1/1680 \\le Vol \\le 1/420$. It is

then intereting to study threefolds of general type with given basket

of singularities and with given fiber structure.

Concerning threefolds with intermediate Kodaira dimension, we

considered the effective Iitaka fibration. For this purpose, it is

interesting to study threefolds with $\\kappa=1$ with given basket of

singularities and abelian fibration.

For explicit birational geoemtry, we will show our result that each

biratioanl map in minimal model program can be factored into a

sequence of following maps (or its inverse)

1. a divisorial contraction to a point of index r with discrepancy 1/r.

2. a blowup along a smooth curve

3. a flop

### 2013/01/11

#### Lectures

10:00-11:00 Room #123 (Graduate School of Math. Sci. Bldg.)

A duality between easy quantum groups and reflection groups (ENGLISH)

**Sven Raum**(KU Leuven)A duality between easy quantum groups and reflection groups (ENGLISH)

#### Lectures

11:15-12:15 Room #123 (Graduate School of Math. Sci. Bldg.)

Some non-uniqueness results for Cartan subalgebras in II$_1$ factors (ENGLISH)

**An Speelman**(KU Leuven)Some non-uniqueness results for Cartan subalgebras in II$_1$ factors (ENGLISH)

#### Lectures

14:00-15:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Structural results for II$_1$ factors of negatively curved groups (ENGLISH)

**Ionut Chifan**(University of Iowa)Structural results for II$_1$ factors of negatively curved groups (ENGLISH)

#### Lectures

15:15-16:15 Room #123 (Graduate School of Math. Sci. Bldg.)

UHF slicing and classification of nuclear $C^*$-algebras (ENGLISH)

**Karen Strung**(Universit\"at M\"unster)UHF slicing and classification of nuclear $C^*$-algebras (ENGLISH)

#### Lectures

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

The generator problem for $C^*$-algebras (ENGLISH)

**Hannes Thiel**(University of Copenhagen)The generator problem for $C^*$-algebras (ENGLISH)

#### GCOE Seminars

10:00-11:00 Room #123 (Graduate School of Math. Sci. Bldg.)

A duality between easy quantum groups and reflection groups (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-1.htm

**Sven Raum**(KU Leuven)A duality between easy quantum groups and reflection groups (ENGLISH)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-1.htm

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