## Seminar information archive

Seminar information archive ～02/01｜Today's seminar 02/02 | Future seminars 02/03～

### 2015/07/23

#### Number Theory Seminar

13:00-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)

Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)

Explicit computation of the number of dormant opers and duality (Japanese)

**Lasse Grimmelt**(University of Göttingen/Waseda University) 13:00-14:00Representation of squares by cubic forms - Estimates for the appearing exponential sums (English)

**Haoyu Hu**(University of Tokyo) 14:15-15:15Ramification and nearby cycles for $\ell$-adic sheaves on relative curves (English)

[ Abstract ]

I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an $\ell$-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.

I will present a new approach for a formula of Deligne and Kato that computes the dimension of the nearby cycle complex of an $\ell$-adic sheaf on a smooth relative curve over a strictly henselian trait such that $p$ is not one of its uniformizer. Deligne considered the case where the sheaf has no vertical ramification and Kato extended the formula to the general case. My approach is based on ramification theory of Abbes and Saito. It computes the nearby cycle complex in terms of the refined Swan conductor. In fact, I compare Abbes-Saito's refined Swan conductor with Kato's Swan conductor with differential values, which is the key ingredient in Kato's formula; the case of rank one sheaves is due to Abbes and Saito. My approach provides also a new independent proof of Deligne-Kato's formula.

**Yasuhiro Wakabayashi**(University of Tokyo) 15:30-16:30Explicit computation of the number of dormant opers and duality (Japanese)

### 2015/07/22

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Recent progress in the classification of amenable $C^*$-algebras

**George Elliott**(Univ. Toronto)Recent progress in the classification of amenable $C^*$-algebras

#### FMSP Lectures

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Recent progress in the classification of amenable C*-algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**George Elliott**(Univ. Toronto)Recent progress in the classification of amenable C*-algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2015/07/21

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Ribbon concordance and 0-surgeries along knots (JAPANESE)

**Keiji Tagami**(Tokyo Institute of Technology)Ribbon concordance and 0-surgeries along knots (JAPANESE)

[ Abstract ]

Akbulut and Kirby conjectured that two knots with

the same 0-surgery are concordant. Recently, Yasui

gave a counterexample of this conjecture.

In this talk, we introduce a technique to construct

non-ribbon concordant knots with the same 0-surgery.

Moreover, we give a potential counterexample of the

slice-ribbon conjecture. This is a joint work with

Tetsuya Abe (Osaka City University, OCAMI).

Akbulut and Kirby conjectured that two knots with

the same 0-surgery are concordant. Recently, Yasui

gave a counterexample of this conjecture.

In this talk, we introduce a technique to construct

non-ribbon concordant knots with the same 0-surgery.

Moreover, we give a potential counterexample of the

slice-ribbon conjecture. This is a joint work with

Tetsuya Abe (Osaka City University, OCAMI).

#### Tuesday Seminar of Analysis

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

Born-Oppenheimer approximation for an atom in constant magnetic fields (Japanese)

**Sohei Ashida**(Department of Mathematics, Kyoto University)Born-Oppenheimer approximation for an atom in constant magnetic fields (Japanese)

[ Abstract ]

We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. Martinez and Sordoni also dealt with such a case but their reduced Hamiltonian includes the vector potential terms. Using the center of mass coordinates and constructing the almost invariant subspace different from theirs, we obtain the reduced Hamiltonian which does not include the vector potential terms. Using the reduced evolution we also obtain the asymptotic expantion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constatnt magnetic fields.

We obtain a reduction scheme for the study of the quantum evolution of an atom in constant magnetic fields using the method developed by Martinez, Nenciu and Sordoni based on the construction of almost invariant subspace. Martinez and Sordoni also dealt with such a case but their reduced Hamiltonian includes the vector potential terms. Using the center of mass coordinates and constructing the almost invariant subspace different from theirs, we obtain the reduced Hamiltonian which does not include the vector potential terms. Using the reduced evolution we also obtain the asymptotic expantion of the evolution for a specific localized initial data, which verifies the straight motion of an atom in constatnt magnetic fields.

#### Lie Groups and Representation Theory

17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

GEOMETRIC STRUCTURE IN SMOOTH DUAL

**Paul Baum**(Penn State University)GEOMETRIC STRUCTURE IN SMOOTH DUAL

[ Abstract ]

Let G be a connected split reductive p-adic group. Examples are GL(n, F) , SL(n, F) , SO(n, F) , Sp(2n, F) , PGL(n, F) where n can be any positive integer and F can be any finite extension of the field Q_p of p-adic numbers. The smooth (or admissible) dual of G is the set of equivalence classes of smooth irreducible representations of G. This talk will first review the theory of the Bernstein center. According to this theory, the smooth dual of G is the disjoint union of subsets known as the Bernstein components. The talk will then explain the ABPS (Aubert-Baum-Plymen-Solleveld) conjecture which states that each Bernstein component is a complex affine variety. Each of these complex affine varieties is explicitly identified as the extended quotient associated to the given Bernstein component.

The ABPS conjecture has been proved for GL(n, F), SO(n, F), and Sp(2n, F).

Let G be a connected split reductive p-adic group. Examples are GL(n, F) , SL(n, F) , SO(n, F) , Sp(2n, F) , PGL(n, F) where n can be any positive integer and F can be any finite extension of the field Q_p of p-adic numbers. The smooth (or admissible) dual of G is the set of equivalence classes of smooth irreducible representations of G. This talk will first review the theory of the Bernstein center. According to this theory, the smooth dual of G is the disjoint union of subsets known as the Bernstein components. The talk will then explain the ABPS (Aubert-Baum-Plymen-Solleveld) conjecture which states that each Bernstein component is a complex affine variety. Each of these complex affine varieties is explicitly identified as the extended quotient associated to the given Bernstein component.

The ABPS conjecture has been proved for GL(n, F), SO(n, F), and Sp(2n, F).

#### Lie Groups and Representation Theory

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

(Japanese)

**Toshiaki Hattori**(Tokyo Institute of Technology)(Japanese)

### 2015/07/17

#### Geometry Colloquium

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

Realization of tropical curves in complex tori (Japanese)

**Takeo Nishinou**(Rikkyo University)Realization of tropical curves in complex tori (Japanese)

[ Abstract ]

Tropical curves are combinatorial object satisfying certain harmonicity condition. They reflect properties of holomorphic curves, and rather precise correspondence is known between tropical curves in real affine spaces and holomorphic curves in toric varieties. In this talk we extend this correspondence to the periodic case. Namely, we give a correspondence between periodic plane tropical curves and holomorphic curves in complex tori. This is a joint work with Tony Yue Yu.

Tropical curves are combinatorial object satisfying certain harmonicity condition. They reflect properties of holomorphic curves, and rather precise correspondence is known between tropical curves in real affine spaces and holomorphic curves in toric varieties. In this talk we extend this correspondence to the periodic case. Namely, we give a correspondence between periodic plane tropical curves and holomorphic curves in complex tori. This is a joint work with Tony Yue Yu.

#### Infinite Analysis Seminar Tokyo

14:00-16:00 Room #002 (Graduate School of Math. Sci. Bldg.)

Classifying simple modules at admissible levels through symmetric polynomials (ENGLISH)

**Simon Wood**(The Australian National University)Classifying simple modules at admissible levels through symmetric polynomials (ENGLISH)

[ Abstract ]

From infinite dimensional Lie algebras such as the Virasoro

algebra or affine Lie (super)algebras one can construct universal

vertex operator algebras. These vertex operator algebras are simple at

generic central charges or levels and only contain proper ideals at so

called admissible levels. The simple quotient vertex operator algebras

at these admissible levels are called minimal model algebras. In this

talk I will present free field realisations of the universal vertex

operator algebras and show how they allow one to elegantly classify

the simple modules over the simple quotient vertex operator algebras

by using a deep connection to symmetric polynomials.

From infinite dimensional Lie algebras such as the Virasoro

algebra or affine Lie (super)algebras one can construct universal

vertex operator algebras. These vertex operator algebras are simple at

generic central charges or levels and only contain proper ideals at so

called admissible levels. The simple quotient vertex operator algebras

at these admissible levels are called minimal model algebras. In this

talk I will present free field realisations of the universal vertex

operator algebras and show how they allow one to elegantly classify

the simple modules over the simple quotient vertex operator algebras

by using a deep connection to symmetric polynomials.

### 2015/07/16

#### Applied Analysis

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

(Japanese)

**Yoshihiro Tonegawa**(Tokyo Institute of Technology)(Japanese)

### 2015/07/14

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

How homoclinic orbits explain some algebraic relations holding in Novikov rings. (ENGLISH)

**Carlos Moraga Ferrandiz**(The University of Tokyo, JSPS)How homoclinic orbits explain some algebraic relations holding in Novikov rings. (ENGLISH)

[ Abstract ]

Given u, a de-Rham cohomology class of degree 1 of a closed manifold M, we consider the space F_u of (closed) Morse 1-forms in this class. In Morse theory, it is important to equip each α in F_u with a descending pseudo-gradient X. The case u=0 yields usual Morse theory, while u ≠ 0 yields Morse-Novikov theory, which is devoted to the understanding of the space of equipped 1-forms (α,X) with α in F_u.

Here, X is a descending pseudo-gradient, which is said to be adapted to α.

The morphism π1(M) → R induced by u (given by the integral of any α in F_u over a loop of M) determines a set of u-negative loops.

We show that for every u-negative g in π1(M), there exists a co-dimension 1 C∞-stratum Sg of F_u which is naturally co-oriented. The stratum Sg is made of elements (α, X) such that X has exactly one homoclinic orbit L whose homotopy class is g.

The goal of this talk is to show that there exists a co-dimension 1 C∞-stratum Sg (0) of Sg which lies in the closure of Sg^2. This result explains geometrically an easy algebraic relation holding in the Novikov ring associated with u.

We will mention how this study generalizes to produce some non-evident symmetric formulas holding in the Novikov ring.

Given u, a de-Rham cohomology class of degree 1 of a closed manifold M, we consider the space F_u of (closed) Morse 1-forms in this class. In Morse theory, it is important to equip each α in F_u with a descending pseudo-gradient X. The case u=0 yields usual Morse theory, while u ≠ 0 yields Morse-Novikov theory, which is devoted to the understanding of the space of equipped 1-forms (α,X) with α in F_u.

Here, X is a descending pseudo-gradient, which is said to be adapted to α.

The morphism π1(M) → R induced by u (given by the integral of any α in F_u over a loop of M) determines a set of u-negative loops.

We show that for every u-negative g in π1(M), there exists a co-dimension 1 C∞-stratum Sg of F_u which is naturally co-oriented. The stratum Sg is made of elements (α, X) such that X has exactly one homoclinic orbit L whose homotopy class is g.

The goal of this talk is to show that there exists a co-dimension 1 C∞-stratum Sg (0) of Sg which lies in the closure of Sg^2. This result explains geometrically an easy algebraic relation holding in the Novikov ring associated with u.

We will mention how this study generalizes to produce some non-evident symmetric formulas holding in the Novikov ring.

#### PDE Real Analysis Seminar

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

Viscosity solutions of Hamilton-Jacobi equations from a dynamical viewpoint (English)

**Lin Wang**(Tsinghua University)Viscosity solutions of Hamilton-Jacobi equations from a dynamical viewpoint (English)

[ Abstract ]

By establishing an implicit variational principle for contact Hamiltonian systems, we detect some properties of viscosity solutions of Hamilton-Jacobi equations of certain Hamilton-Jacobi equations depending on unknown functions, including large time behavior and regularity on certain sets. Besides, I will talk about some connections with contact geometry, thermodynamics and nonholonomic mechanics.

By establishing an implicit variational principle for contact Hamiltonian systems, we detect some properties of viscosity solutions of Hamilton-Jacobi equations of certain Hamilton-Jacobi equations depending on unknown functions, including large time behavior and regularity on certain sets. Besides, I will talk about some connections with contact geometry, thermodynamics and nonholonomic mechanics.

#### Tuesday Seminar of Analysis

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

Small-time Asymptotics for Subelliptic Heat Kernels (English)

**Li Yutian**(Department of Mathematics, Hong Kong Baptist University)Small-time Asymptotics for Subelliptic Heat Kernels (English)

[ Abstract ]

Subelliptic operators are the natural generalizations of the Laplace- Beltrami operators, and they play important roles in geometry, several complex variables, probability and physics. As in the classical spectral theory for the elliptic operators, some geometrical properties of the induced subRiemannian geometry can be extracted from the analysis of the heat kernels for subelliptic operators. In this talk we shall review the recent progress in the heat kernel asymptotics for subelliptic operators. We concentrate on the small-time asymptotics of the heat kernel on the diagonal, or equivalently, the asymptotics for the trace. Our interest is to find the exact form of the leading term, and this will lead to a Weyl’s asymptotic formula for the subelliptic operators. This is a joint work with Professor Der-Chen Chang.

Subelliptic operators are the natural generalizations of the Laplace- Beltrami operators, and they play important roles in geometry, several complex variables, probability and physics. As in the classical spectral theory for the elliptic operators, some geometrical properties of the induced subRiemannian geometry can be extracted from the analysis of the heat kernels for subelliptic operators. In this talk we shall review the recent progress in the heat kernel asymptotics for subelliptic operators. We concentrate on the small-time asymptotics of the heat kernel on the diagonal, or equivalently, the asymptotics for the trace. Our interest is to find the exact form of the leading term, and this will lead to a Weyl’s asymptotic formula for the subelliptic operators. This is a joint work with Professor Der-Chen Chang.

#### Lie Groups and Representation Theory

17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)

MORITA EQUIVALENCE REVISITED

**Paul Baum**(Penn State University)MORITA EQUIVALENCE REVISITED

[ Abstract ]

Let X be a complex affine variety and k its coordinate algebra. A k- algebra is an algebra A over the complex numbers which is a k-module (with an evident compatibility between the algebra structure of A and the k-module structure of A). A is not required to have a unit. A k-algebra A is of finite type if as a k-module A is finitely generated. This talk will review Morita equivalence for k-algebras and will then introduce --- for finite type k-algebras ---a weakening of Morita equivalence called geometric equivalence. The new equivalence relation preserves the primitive ideal space (i.e. the set of isomorphism classes of irreducible A-modules) and the periodic cyclic homology of A. However, the new equivalence relation permits a tearing apart of strata in the primitive ideal space which is not allowed by Morita equivalence.

Let G be a connected split reductive p-adic group, The ABPS (Aubert- Baum-Plymen-Solleveld) conjecture states that the finite type algebra which Bernstein assigns to any given Bernstein component in the smooth dual of G, is geometrically equivalent to the coordinate algebra of the associated extended quotient. The second talk will give an exposition of the ABPS conjecture.

Let X be a complex affine variety and k its coordinate algebra. A k- algebra is an algebra A over the complex numbers which is a k-module (with an evident compatibility between the algebra structure of A and the k-module structure of A). A is not required to have a unit. A k-algebra A is of finite type if as a k-module A is finitely generated. This talk will review Morita equivalence for k-algebras and will then introduce --- for finite type k-algebras ---a weakening of Morita equivalence called geometric equivalence. The new equivalence relation preserves the primitive ideal space (i.e. the set of isomorphism classes of irreducible A-modules) and the periodic cyclic homology of A. However, the new equivalence relation permits a tearing apart of strata in the primitive ideal space which is not allowed by Morita equivalence.

Let G be a connected split reductive p-adic group, The ABPS (Aubert- Baum-Plymen-Solleveld) conjecture states that the finite type algebra which Bernstein assigns to any given Bernstein component in the smooth dual of G, is geometrically equivalent to the coordinate algebra of the associated extended quotient. The second talk will give an exposition of the ABPS conjecture.

### 2015/07/13

#### Seminar on Geometric Complex Analysis

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

$L^2$ cohomology and deformation of Einstein metrics on strictly pseudo convex domains

**Yoshihiko Matsumoto**(Tokyo Institute of Technology)$L^2$ cohomology and deformation of Einstein metrics on strictly pseudo convex domains

[ Abstract ]

Consider a bounded domain of a Stein manifold, with strictly pseudo convex smooth boundary, endowed with an ACH-Kähler metric (examples being domains of $\mathbb{C}^n$ with their Bergman metrics or Cheng-Yau’s Einstein metrics). We give a vanishing theorem on the $L^2$ $\overline{\partial}$-cohomology group with values in the holomorphic tangent bundle. As an application, Einstein perturbations of the Cheng-Yau metric are discussed.

Consider a bounded domain of a Stein manifold, with strictly pseudo convex smooth boundary, endowed with an ACH-Kähler metric (examples being domains of $\mathbb{C}^n$ with their Bergman metrics or Cheng-Yau’s Einstein metrics). We give a vanishing theorem on the $L^2$ $\overline{\partial}$-cohomology group with values in the holomorphic tangent bundle. As an application, Einstein perturbations of the Cheng-Yau metric are discussed.

#### Tokyo Probability Seminar

16:30-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

On interacting particle systems in beta random matrix theory

Random field of gradients and elasticity

**Mykhaylo Shkolnikov**(Mathematics Department, Princeton University) 16:30-17:20On interacting particle systems in beta random matrix theory

[ Abstract ]

I will first introduce multilevel Dyson Brownian motions and review how those extend to the setting of beta random matrix theory. Then, I will describe a connection between multilevel Dyson Brownian motions and interacting particle systems on the real line with local interactions. This is the first connection of this kind for values of beta different from 1 and 2. Based on joint work with Vadim Gorin.

I will first introduce multilevel Dyson Brownian motions and review how those extend to the setting of beta random matrix theory. Then, I will describe a connection between multilevel Dyson Brownian motions and interacting particle systems on the real line with local interactions. This is the first connection of this kind for values of beta different from 1 and 2. Based on joint work with Vadim Gorin.

**Stefan Adams**(Mathematics Institute, Warwick University) 17:30-18:20Random field of gradients and elasticity

[ Abstract ]

Random fields of gradients are a class of model systems arising in the studies of random interfaces, random geometry, field theory, and elasticity theory. These random objects pose challenging problems for probabilists as even an a priori distribution involves strong correlations, and are likely to be an universal class of models combining probability, analysis and physics in the study of critical phenomena. They emerge in the following three areas, effective models for random interfaces, Gaussian Free Fields (scaling limits), and mathematical models for the Cauchy-Born rule of materials, i.e., a microscopic approach to nonlinear elasticity. The latter class of models requires that interaction energies are non-convex functions of the gradients. Open problems over the last decades include unicity of Gibbs measures, the scaling to GFF and strict convexity of the free energy. We present in the talk first results for the free energy and the scaling limit at low temperatures using Gaussian measures and rigorous renormalisation group techniques yielding an analysis in terms of dynamical systems. The key ingredient is a finite range decomposition for parameter dependent families of Gaussian measures. (partly joint work with S. Mueller & R. Kotecky)

Random fields of gradients are a class of model systems arising in the studies of random interfaces, random geometry, field theory, and elasticity theory. These random objects pose challenging problems for probabilists as even an a priori distribution involves strong correlations, and are likely to be an universal class of models combining probability, analysis and physics in the study of critical phenomena. They emerge in the following three areas, effective models for random interfaces, Gaussian Free Fields (scaling limits), and mathematical models for the Cauchy-Born rule of materials, i.e., a microscopic approach to nonlinear elasticity. The latter class of models requires that interaction energies are non-convex functions of the gradients. Open problems over the last decades include unicity of Gibbs measures, the scaling to GFF and strict convexity of the free energy. We present in the talk first results for the free energy and the scaling limit at low temperatures using Gaussian measures and rigorous renormalisation group techniques yielding an analysis in terms of dynamical systems. The key ingredient is a finite range decomposition for parameter dependent families of Gaussian measures. (partly joint work with S. Mueller & R. Kotecky)

### 2015/07/11

#### Harmonic Analysis Komaba Seminar

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

An intrinsic square function on weighted Herz spaces with variable exponent

(日本語)

Remarks on the strong maximum principle involving p-Laplacian

(日本語)

**Mitsuo Izuki**(Okayama University) 13:30 -15:00An intrinsic square function on weighted Herz spaces with variable exponent

(日本語)

**Toshio Horiuchi**(Ibaraki University) 15:30 -17:00Remarks on the strong maximum principle involving p-Laplacian

(日本語)

### 2015/07/10

#### thesis presentations

13:30-14:45 Room #128 (Graduate School of Math. Sci. Bldg.)

On stability of viscosity solutions under non-Euclidean metrics（非ユークリッド距離構造の下での粘性解の安定性） (JAPANESE)

**中安 淳**(東京大学大学院数理科学研究科)On stability of viscosity solutions under non-Euclidean metrics（非ユークリッド距離構造の下での粘性解の安定性） (JAPANESE)

### 2015/07/09

#### Infinite Analysis Seminar Tokyo

15:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

An extension of the LMO functor and formal Gaussian integrals (JAPANESE)

On the relative number of ends of higher dimensional Thompson groups (JAPANESE)

**Yuta Nozaki**(Graduate School of Mathematical Sciences, the University of Tokyo) 15:00-16:30An extension of the LMO functor and formal Gaussian integrals (JAPANESE)

[ Abstract ]

Cheptea, Habiro and Massuyeau introduced the LMO functor as an

extension of the LMO invariant of closed 3-manifolds.

The LMO functor is “the monoidal category of Lagrangian cobordisms

between surfaces with at most one boundary component” to “the monoidal

category of certain Jacobi diagrams”.

In this talk, we extend the LMO functor to the case of any number of

boundary components.

In particular, we focus on a formal Gaussian integral, that is an

essential tool to construct the LMO functor.

Cheptea, Habiro and Massuyeau introduced the LMO functor as an

extension of the LMO invariant of closed 3-manifolds.

The LMO functor is “the monoidal category of Lagrangian cobordisms

between surfaces with at most one boundary component” to “the monoidal

category of certain Jacobi diagrams”.

In this talk, we extend the LMO functor to the case of any number of

boundary components.

In particular, we focus on a formal Gaussian integral, that is an

essential tool to construct the LMO functor.

**Motoko Kato**(Graduate School of Mathematical Sciences, the University of Tokyo) 17:00-18:30On the relative number of ends of higher dimensional Thompson groups (JAPANESE)

[ Abstract ]

In 2004, Brin defined n−dimensional Thompson group nV for every natural number n ≥ 1. nV is a generalization of the Thompson group V . The Thompson group V can be described as a subgroup of the homeomorphism group of the Cantor set C. In this point of view, nV is a subgroup of the homeomorphism group of Cn. We prove that the number of ends of nV is equal to 1 and there is a subgroup of nV such that the relative number of ends is ∞. As a corollary of the second result, for each n, nV has Haagerup property and it can not be the fundamental group of a compact K ̈ahler manifold. These results are the generalizations of the corresponding results of Farley, who studied the Thompson group V .

In 2004, Brin defined n−dimensional Thompson group nV for every natural number n ≥ 1. nV is a generalization of the Thompson group V . The Thompson group V can be described as a subgroup of the homeomorphism group of the Cantor set C. In this point of view, nV is a subgroup of the homeomorphism group of Cn. We prove that the number of ends of nV is equal to 1 and there is a subgroup of nV such that the relative number of ends is ∞. As a corollary of the second result, for each n, nV has Haagerup property and it can not be the fundamental group of a compact K ̈ahler manifold. These results are the generalizations of the corresponding results of Farley, who studied the Thompson group V .

### 2015/07/08

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Conformal field theory, subfactors and planar algebras

**Marcel Bischoff**(Vanderbilt Univ.)Conformal field theory, subfactors and planar algebras

#### FMSP Lectures

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Conformal field theory, subfactors and planar algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Marcel Bischoff**(Vanderbilt Univ.)Conformal field theory, subfactors and planar algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2015/07/07

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Representation varieties detect essential surfaces (JAPANESE)

**Takahiro Kitayama**(Tokyo Institute of Technology)Representation varieties detect essential surfaces (JAPANESE)

[ Abstract ]

Extending Culler-Shalen theory, Hara and I presented a way to construct

certain kinds of branched surfaces (possibly without any branch) in a 3-

manifold from an ideal point of a curve in the SL_n-character variety.

There exists an essential surface in some 3-manifold known to be not

detected in the classical SL_2-theory. We show that every essential

surface in a 3-manifold is given by the ideal point of a line in the SL_

n-character variety for some n. The talk is partially based on joint

works with Stefan Friedl and Matthias Nagel, and also with Takashi Hara.

Extending Culler-Shalen theory, Hara and I presented a way to construct

certain kinds of branched surfaces (possibly without any branch) in a 3-

manifold from an ideal point of a curve in the SL_n-character variety.

There exists an essential surface in some 3-manifold known to be not

detected in the classical SL_2-theory. We show that every essential

surface in a 3-manifold is given by the ideal point of a line in the SL_

n-character variety for some n. The talk is partially based on joint

works with Stefan Friedl and Matthias Nagel, and also with Takashi Hara.

### 2015/07/06

#### Seminar on Geometric Complex Analysis

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

On the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (JAPANESE)

**Akio Kodama**On the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (JAPANESE)

[ Abstract ]

In this talk, we first review the structure of holomorphic automorphism groups of generalized complex ellipsoids and, as an application of this, we clarify completely the structure of generalized Hartogs triangles. Finally, if possible, I will mention some known results on proper holomorphic self-mappings of generalized complex ellipsoids, generalized Hartogs triangles, and discuss a related question to these results.

In this talk, we first review the structure of holomorphic automorphism groups of generalized complex ellipsoids and, as an application of this, we clarify completely the structure of generalized Hartogs triangles. Finally, if possible, I will mention some known results on proper holomorphic self-mappings of generalized complex ellipsoids, generalized Hartogs triangles, and discuss a related question to these results.

### 2015/07/03

#### Geometry Colloquium

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

Proper actions of reductive groups on pseudo-Riemannian symmetric spaces and its compact dual. (日本語)

**Takayuki OKUDA**(HIroshima University)Proper actions of reductive groups on pseudo-Riemannian symmetric spaces and its compact dual. (日本語)

[ Abstract ]

Let G be a non-compact semisimple Lie group. We take a pair of symmetric pairs (G,H) and (G,L) such that the diagonal action of G on G/H \times G/L is proper. In this talk, we show that by taking ``the compact dual of triple (G,H,L)'', we obtain a compact symmetric space M = U/K and its reflective submanifolds S_1 and S_2 satisfying that the intersection of S_1 and gS_2 is discrete in M for any g in U. In particular, we give a classification of such triples (G,H,L).

Let G be a non-compact semisimple Lie group. We take a pair of symmetric pairs (G,H) and (G,L) such that the diagonal action of G on G/H \times G/L is proper. In this talk, we show that by taking ``the compact dual of triple (G,H,L)'', we obtain a compact symmetric space M = U/K and its reflective submanifolds S_1 and S_2 satisfying that the intersection of S_1 and gS_2 is discrete in M for any g in U. In particular, we give a classification of such triples (G,H,L).

### 2015/07/01

#### Operator Algebra Seminars

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Approximate unitary equivalence of finite index endomorphisms of the AFD

factors

**Koichi Shimada**(Univ. Tokyo)Approximate unitary equivalence of finite index endomorphisms of the AFD

factors

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